01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
11.03.1955
Phone:
+7 (495) 250 78 56
E-mail:
Keywords:
mathematics.
UDC:
517.53, 517.3, 517.5, 517.51, 517.9, 530.145
Subject:
Mathematics.
Main publications:
A. I. Aptekarev, S. A. Denisov, D. N. Tulyakov, “On a problem by Steklov”, J. Amer. Math. Soc., 29 (2016), 1117–1165
A. I. Aptekarev, “The Mhaskar–Saff Variational Principle and Location of the Shocks of Certain Hyperbolic Equations”, Contemporary Mathematics, 661 (2016), 167–186
A. I. Aptekarev, M. L. Yattselev, “Pade approximants for functions with branch points – strong asymptotics of Nuttall–Stahl polynomials”, Acta Math., 215 (2015), 217–280
A. I. Aptekarev, “Spectral Problems of High-Order Recurrences”, Amer. Math. Soc. Transl., 233 (2014), 43–61
A. I. Aptekarev, D. N. Tulyakov, “Asymptotics of Meixner polynomials and Christoffel-Darboux kernels”, Trans. Moscow Math. Soc., 2012, 67–106
A. I. Aptekarev, P. M. Bleher, A. B. J. Kuijlaars, “Large $n$ limit of Gaussian random matrices with external source. II”, Comm. Math. Phys., 259:2 (2005), 367–389
A. I. Aptekarev, “Sharp constants for rational approximations of analytic functions”, Sb. Math., 193:1 (2002), 1–72
A. I. Aptekarev, “Strong asymptotics of multiply orthogonal polynomials for Nikishin systems”, Sb. Math., 190:5 (1999), 631–669
A. I. Aptekarev, “A direct proof for Trefethen's conjecture”, Methods of Approximation Theory in Complex Analysis and Mathematical Physics, May 13–24, 1991, Leningrad, Lecture Notes in Math., 1550, Springer, Berlin, 1993, 147–148
A. I. Aptekarev, “Asymptotics of orthogonal polynomials in a neighborhood of the endpoints of the interval of orthogonality”, Russian Acad. Sci. Sb. Math., 76:1 (1993), 35–50
A. I. Aptekarev, “Asymptotics of simultaneously orthogonal polynomials in the Angelesco case”, Math. USSR-Sb., 64:1 (1989), 57–84
A. I. Aptekarev, S. A. Denisov, M. L. Yattselev, “Selfadjoint Jacobi matrices on graphs and multiple orthogonal polynomials”, Keldysh Institute preprints, 2018
2.
Kompleksnyi analiz, matematicheskaya fizika i prilozheniya, Sbornik statei, Tr. MIAN, 301, ed. A. I. Aptekarev, M. O. Katanaev, S. P. Suetin, MAIK «Nauka/Interperiodika», M., 2018
3.
L. A. Aksent'ev, A. I. Aptekarev, A. M. Bikchentaev, V. V. Goryainov, V. N. Dubinin, A. M. Elizarov, I. R. Kayumov, A. Laptev, S. R. Nasyrov, D. V. Prokhorov, A. G. Sergeev, V. D. Stepanov, “arid Gabidinovich Avkhadiev (on his 70th birthday)”, Uspekhi Mat. Nauk, 73:1(439) (2018), 187–190
2017
4.
A. I. Aptekarev, A. I. Bogolyubskii, M. Yattselev, “Convergence of ray sequences of Frobenius-Padé approximants”, Sb. Math., 208:3 (2017), 313–334
5.
A. I. Aptekarev, M. A. Lapik, Yu. N. Orlov, “Asymptotic behavior of the spectrum of combination scattering at Stokes phonons”, Theoret. and Math. Phys., 193:1 (2017), 1480–1497
6.
A. I. Aptekarev, G. López Lagomasino, A. Martínez-Finkelshtein, “On Nikishin systems with discrete components and weak asymptotics of multiple orthogonal polynomials”, Russian Math. Surveys, 72:3 (2017), 389–449
7.
A. I. Aptekarev, D. N. Tulyakov, “The Hesse coordinates for an algebraic cubic curve”, Keldysh Institute preprints, 2017
8.
A. I. Aptekarev, A. Draux, D. N. Tulyakov, “On asymptotics of the sharp constants of the Markov–Bernshtein inequalities for the Sobolev spaces with coherent weights”, Preprinty IPM im. M. V. Keldysha, 2017, 59 , 20 pp.
9.
A. I. Aptekarev, A. L. Afendikov, F. I. Ataullakhanov, N. K. Balabaev, V. N. Biktashev, I. V. Biktasheva, R. M. Borisyuk, N. D. Vvedenskaya, R. D. Dagkesamanskii, Yu. G. Zarkhin, Yu. S. Ilyashenko, V. D. Lakhno, V. Yu. Lunin, N. L. Lunina, E. V. Nikolaev, V. S. Posvyanskii, M. A. Roitberg, V. S. Ryaben'kii, L. B. Ryashko, Ya. G. Sinai, V. M. Tikhomirov, A. A. Tokarev, A. G. Urzhumtsev, A. I. Khibnik, “To the memory of Èmmanuil Èl'evich Shnol'”, Russian Math. Surveys, 72:1 (2017), 185–198
10.
M. V. Abakumov, A. I. Aptekarev, M. P. Galanin, M. K. Kerimov, O. S. Mazhorova, G. G. Malinetskii, S. I. Mukhin, Yu. A. Poveschenko, B. N. Chetverushkin, V. M. Chechetkin, Zh. Vychisl. Mat. Mat. Fiz., 57:7 (2017), 1231–1240
2016
11.
A. I. Aptekarev, S. A. Denisov, “The Steklov problem and estimates for orthogonal polynomials with $A_p(\mathbb{T})$ weights”, Keldysh Institute preprints, 2016, 40–19
12.
Alexander I. Aptekarev, Maxim Derevyagin, Hiroshi Miki, Walter Van Assche, “Multidimensional Toda Lattices: Continuous and Discrete Time”, SIGMA, 12 (2016), 54, 54–30 , 30 pp., arXiv: 1511.08098 (cited: 2) (cited: 2) (cited: 2)
13.
A. I. Aptekarev, D. N. Tulyakov, “Nuttall's Abelian integral on the Riemann surface of the cube root of a polynomial of degree 3”, Izv. Math., 80:6 (2016), 997–1034 (cited: 2) (cited: 1)
14.
A. I. Aptekarev, S. A. Denisov, D. N. Tulyakov, “On a problem by Steklov”, J. Amer. Math. Soc., 29 (2016), 1117–1165 (cited: 3) (cited: 1) (cited: 3)
15.
A. I. Aptekarev, M. Derevyagin, W. Van Assche, “Discrete integrable systems generated by Hermite–Padé approximants”, Nonlinearity, 29 (2016), 1487–1506 (cited: 1) (cited: 1) (cited: 1)
16.
A. I. Aptekarev, “The Mhaskar–Saff Variational Principle and Location of the Shocks of Certain Hyperbolic Equations”, Contemporary Mathematics, 661 (2016), 167–186 (cited: 1) (cited: 2)
17.
A. I. Aptekarev, D. N. Tulyakov, I. V. Toranzo, J. S. Dehesa, “Renyi entropies of the highly-excited states of multidimensional harmonic oscillators by use of strong Laguerre asymptotics”, Eur. Phys. J. B, 89:85 (2016) , 13 pp. (cited: 1)
18.
A. I. Aptekarev, J. S. Geronimo, “Measures for orthogonal polynomials with unbounded recurrence coefficients”, Journal of Approximation Theory, 207 (2016), 339–347 (cited: 1) (cited: 2) (cited: 2)
19.
A. I. Aptekarev, M. L. Yattselev, “Approximations of algebraic functions by rational ones — functional analogues of diophantine approximants”, Keldysh Institute preprints, 2016
20.
A. I. Aptekarev, A. B. Batkhin, A. D. Bruno, “Vladimir Igorevich Parusnikov”, Chebyshevskii Sb., 17:1 (2016), 286–298
2015
21.
A. I. Aptekarev, S. A. Denisov, D. N. Tulyakov, “V.A. Steklov's Problem of Estimating the Growth of Orthogonal Polynomials”, Proc. Steklov Inst. Math., 289 (2015), 72–95
22.
A. I. Aptekarev, D. N. Tulyakov, “The Saturation Regime of Meixner Polynomials and the Discrete Bessel Kernel”, Math. Notes, 98:1 (2015), 180–184 (cited: 1)
23.
A. I. Aptekarev, D. N. Tulyakov, “Asymptotics of $L_p$-norms of Laguerre polynomials and entropic moments of $D$-dimensional oscillator”, Preprinty IPM im. M. V. Keldysha, 2015, 41–15 (cited: 1)
24.
A. I. Aptekarev, D. N. Tulyakov, “Asymptotics of $L_p$-norms of Laguerre polynomials”, Russian Math. Surveys, 70:5 (2015), 955–957 (cited: 1) (cited: 1)
25.
A. I. Aptekarev, S. A. Denisov, M. Yattselev, “Completely integrable on $\mathbb{Z}_+^d$ potentials for electromagnetic Schrodinger operator: rays asymptotics and scattering problem”, Keldysh Institute preprints, 2015, 88–20
26.
A. I. Aptekarev, D. N. Tulyakov, M. Yattselev, “On the Parametrization of a Certain Algebraic Curve of Genus 2”, Math. Notes, 98:5 (2015), 843–846 (cited: 1)
27.
A. I. Aptekarev, M. L. Yattselev, “Pade approximants for functions with branch points – strong asymptotics of Nuttall–Stahl polynomials”, Acta Math., 215 (2015), 217–280 (cited: 5) (cited: 2) (cited: 3)
28.
A. I. Aptekarev, A. Draux, V. A. Kalyagin, D. N. Tulyakov, “Asymptotics of sharp constants of Markov–Bernstein inequalities in integral norm with jacobi weight”, Proceedings of the American Mathematical Society, 143:9 (2015), 3847–3862 (cited: 1) (cited: 1)
29.
A. I. Aptekarev, M. Derevyagin, W. Van Assche, “On $2D$ discrete Schrödinger operators associated with multiple orthogonal polynomials”, J. Phys. A: Math. Theor., 48:6 (2015), 065201 , 16 pp. (cited: 1) (cited: 2) (cited: 2)
30.
A. I. Aptekarev, G. Lopes-Lagomasino, A. Martines-Finkelshtein, “Cilnaya asimptotika sovmestno ortogonalnykh mnogochlenov Pollacheka”, Doklady Akademii Nauk, 465:4 (2015), 393–397
31.
A. I. Aptekarev, D. N. Toulyakov, W. Van Assche, “Hyperelliptic uniformization of algebraic curves of the third order”, Journal Computational and Applied Mathematics, 284 (2015), 38–49 (cited: 3) (cited: 4)
2014
32.
A. I. Aptekarev, D. N. Tulyakov, “Abelian integral of Nuttall on the Riemann surface of the cubic root of the third degree polynomial”, Keldysh Institute preprints, 2014, 15–25
33.
A. I. Aptekarev, D. N. Tulyakov, “The leading term of the Plancherel-Rotach asymptotic formula for solutions of recurrence relations”, Sb. Math., 205:12 (2014), 1696–1719 (cited: 4) (cited: 1) (cited: 1) (cited: 1)
34.
A. I. Aptekarev, A. I. Bogolyubsky, “Matrix Riemann–Hilbert problems for Pade approximants of orthogonal expansions”, Keldysh Institute preprints, 2014, 103–16
35.
A. I. Aptekarev, “Spectral Problems of High-Order Recurrences”, Amer. Math. Soc. Transl., 233 (2014), 43–61 (cited: 1)
36.
A. I. Aptekarev, J. Arvesu, “Asymptotics for Multiple Meixner Polynomials”, Journal of Mathematical Analysis and Applications, 411 (2014), 485–505 (cited: 3) (cited: 5) (cited: 4)
37.
A. I. Aptekarev, A. L. Afendikov, V. M. Buchstaber, S. K. Godunov, A. B. Zhizhchenko, V. V. Kozlov, A. I. Maslov, V. P. Platonov, V. F. Tishkin, L. D. Faddeev, “Boris Nikolaevich Chetverushkin (on his 70th birthday)”, Russian Math. Surveys, 69:2 (2014), 387–392
38.
A. I. Aptekarev, P. A. Borodin, B. S. Kashin, Yu. V. Nesterenko, P. V. Paramonov, A. V. Pokrovskii, A. G. Sergeev, A. T. Fomenko, “Evgenii Prokof'evich Dolzhenko (on his 80th birthday)”, Russian Math. Surveys, 69:6 (2014), 1143–1148
39.
A. Aptekarev, P. Nevai, V. Totik, “In memoriam: Herbert Stahl, August 3, 1942–April 22, 2013”, Journal Approximation Theory, 183 (2014), A1–A26 (cited: 1) (cited: 1)
2013
40.
A. I. Aptekarev, D. N. Tulyakov, “Main term of asymptotics of the solutions of the four-terms recurrence relations”, Keldysh Institute preprints, 2013, 1–20
41.
A. I. Aptekarev, V. S. Buyarov, “On the Resolvent of the Gauss Operator”, Math. Notes, 94:4 (2013), 590–593
42.
A. I. Aptekarev, S. A. Denisov, D. N. Tulyakov, “Fejer convolutions for an extremal problem in the Steklov class”, Preprinty IPM, 2013, 76–19
2012
43.
A. I. Aptekarev, D. N. Tulyakov, “Asymptotics of Meixner polynomials and Christoffel-Darboux kernels”, Trans. Moscow Math. Soc., 2012, 67–106 (cited: 3)
44.
A. I. Aptekarev, D. N. Tulyakov, “Geometry of Hermite-Padé approximants for system of functions $\{f,f^2\}$ with three branch points”, Preprinty IPM, 2012, 77–25 (cited: 5)
45.
A. I. Aptekarev, D. N. Tulyakov, “Asymptotics of $L_p$-norms of Hermite polynomials”, Preprinty IPM, 2012, 70–22
46.
A. I. Aptekarev, R. È. Akhmedov, V. S. Buyarov, “Representation of the Gauss-Babenko operator in the power series basis”, Keldysh Institute preprints, 2012, 69–23
47.
A. I. Aptekarev, “Integrable Semidiscretization of Hyperbolic Equations – “Computational” Dispersion and Multidimensional Perspective”, Keldysh Institute preprints, 2012, 20–28
48.
A. I. Aptekarev, J. S. Dehesa, P. Sánchez-Moreno, D. N. Tulyakov, “Asymptotics of $Lp$-norms of Hermite polynomials and Renyi entropy of Rydberg oscillator states”, Contemporary Mathematics, 578 (2012), 19–29 (cited: 2)
49.
A. I. Aptekarev, J. S. Dehesa, P. Sánchez-Moreno, D. N. Tulyakov, “Rényi entropy of the infinite well potential in momentum space and Dirichlet-like trigonometric functionals”, J. Math. Chem., 50 (2012), 1079–1090 (cited: 1) (cited: 1) (cited: 1)
2011
50.
A. I. Aptekarev, D. N. Tulyakov, “Asymptotic regimes in saturation zones for the C-D-kernels for an ensemble of Meixner orthogonal polynomials”, Russian Math. Surveys, 66:1 (2011), 173–175
51.
A. I. Aptekarev, V. G. Lysov, D. N. Tulyakov, “Random matrices with external source and the asymptotic behaviour of multiple orthogonal polynomials”, Sb. Math., 202:2 (2011), 155–206 (cited: 20) (cited: 13) (cited: 13) (cited: 12)
52.
A. I. Aptekarev, A. Kuijlaars, “Hermite–Padé approximations and multiple orthogonal polynomial ensembles”, Russian Math. Surveys, 66:6 (2011), 1133–1199 (cited: 1) (cited: 23) (cited: 16) (cited: 16) (cited: 16)
53.
A. I. Aptekarev, V. I. Buslaev, A. Martínez-Finkelshtein, S. P. Suetin, “Padé approximants, continued fractions, and orthogonal polynomials”, Russian Math. Surveys, 66:6 (2011), 1049–1131 (cited: 2) (cited: 26) (cited: 17) (cited: 17) (cited: 19)
54.
A. I. Aptekarev, A. L. Afendikov, B. N. Chetverushkin, “M. V. Keldysh, scientist and statesman (on the centenary of his birth)”, Russian Math. Surveys, 66:1 (2011), 183–196
55.
A. I. Aptekarev, G. López Lagomasino, E. B. Saff, V. Totik, H. Stahl, “Andrei Aleksandrovich Gonchar (on his 80th birthday)”, Russian Math. Surveys, 66:6 (2011), 1209–1216 (cited: 2)
56.
A. I. Aptekarev, “Matematicheskii portret”, Priroda, 2011, no. 2, 42–49
2010
57.
A. I. Aptekarev, V. G. Lysov, “Systems of Markov functions generated by graphs and the asymptotics of their Hermite-Padé approximants”, Sb. Math., 201:2 (2010), 183–234 (cited: 23) (cited: 21) (cited: 21) (cited: 22)
58.
A. I. Aptekarev, J. S. Dehesa, A. Martínez-Finkelshtein, R. J. Yáñez, “Quantum expectation values of $D$-dimensional Rydberg hydrogenic states by use of Laguerre and Gegenbauer asymptotics”, J. Phys. A, 43:14 (2010), 145204 , 10 pp. (cited: 2) (cited: 8) (cited: 8)
59.
A. I. Aptekarev, J. S. Dehesa, A. Martinez-Finkelshtein, “Asymptotics of orthogonal polynomial's entropy”, J. Comput. Appl. Math., 233:6 (2010), 1355–1365 (cited: 9) (cited: 17) (cited: 13) (cited: 19)
2009
60.
A. I. Aptekarev, V. G. Lysov, D. N. Tulyakov, “Global eigenvalue distribution regime of random matrices with an anharmonic potential and an external source”, Theoret. and Math. Phys., 159:1 (2009), 448–468 (cited: 7) (cited: 10) (cited: 10) (cited: 7)
61.
A. I. Aptekarev, V. A. Kalyagin, V. G. Lysov, D. N. Toulyakov, “Equilibrium of vector potentials and uniformization of the algebraic curves of genus 0”, J. Comput. Appl. Math., 233:3 (2009), 602–616 (cited: 6) (cited: 10) (cited: 8) (cited: 7)
62.
A. I. Aptekarev, D. N. Tulyakov, “On the determinant of an integral lattice generated by rational approximants of the Euler constant”, Tr. Mosk. Mat. Obs., 70 (2009), 329–345 (cited: 1)
63.
A. I. Aptekarev, V. A. Kalyagin, E. B. Saff, “Higher-order three-term recurrences and asymptotics of multiple orthogonal polynomials”, Constr. Approx., 30:2 (2009), 175–223 (cited: 11) (cited: 18) (cited: 23) (cited: 20)
64.
A. I. Aptekarev, J. S. Dehesa, A. Martínez-Finkelshtein, R. J. Yáñez, “Discrete entropies of orthogonal polynomials”, Constr. Approx., 30:1 (2009), 93–119 (cited: 6) (cited: 5) (cited: 5) (cited: 4)
2008
65.
A. I. Aptekarev, “Asymptotics of Hermite-Padé approximants for a pair of functions with branch points”, Dokl. Math., 78:2 (2008), 717–719 (cited: 25) (cited: 15) (cited: 15)
66.
A. I. Aptekarev, J. S. Geronimo, Van W. Assche, “Varying weights for orthogonal polynomials with monotonically varying recurrence coefficients”, J. Approx. Theory, 150:2 (2008), 214–238 (cited: 2) (cited: 4) (cited: 2) (cited: 3)
67.
A. I. Aptekarev, “Matrix Riemann–Hilbert analysis for the case of higher genus — asymptotics of polynomials orthogonal on a system of intervals”, Preprinty IPM, 2008, 28–23 (cited: 1)
2011
68.
A. I. Aptekarev, “Preface”, Proc. Steklov Inst. Math., 272, suppl. 2 (2011), 138–141 (cited: 2) (cited: 1)
2007
69.
A. Aptekarev, R. Khabibullin, “Asymptotic series for polynomials orthogonal with respect to a complex varying weight”, Tr. Mosk. Mat. Obs., 68 (2007), 3–43 (cited: 4)
70.
A. I. Aptekarev, A. B. J. Kuijlaars, Van W. Assche, “Asymptotics of Hermite-Padé rational approximants for two analytic functions with separated pairs of branch points (case of genus 0)”, Int. Math. Res. Pap. IMRP, 2007, no. 4, Art. ID rpm007, 128 pp. (2008) (cited: 1)
2011
71.
A. I. Aptekarev, D. N. Tulyakov, “Four-termed recurrence relations for $\gamma$-forms”, Proc. Steklov Inst. Math., 272, suppl. 2 (2011), 157–161 (cited: 1)
72.
A. I. Aptekarev, V. G. Lysov, “Asymptotics of $\gamma$-forms jointly generated by orthogonal polynomials”, Proc. Steklov Inst. Math., 272, suppl. 2 (2011), 168–173 (cited: 2)
2007
73.
A. I. Aptekarev, V. G. Lysov, D. N. Tulyakov, “Three-sheeted Riemann surfaces of genus 0 with fixed projections of the branch points”, Keldysh Institute preprints, 2007, 13–21
74.
M. S. Agranovich, A. I. Aptekarev, A. L. Afendikov, N. D. Vvedenskaya, M. I. Vishik, S. G. Gindikin, M. M. Malamud, B. P. Paneah, E. V. Radkevich, V. M. Tikhomirov, A. R. Shirikyan, “Leonid Romanovich Volevich (obituary)”, Russian Math. Surveys, 62:6 (2007), 1187–1190
75.
Ratsionalnye priblizheniya postoyannoi Eilera i rekurrentnye sootnosheniya, Sbornik statei, Sovr. probl. matem., 9, ed. A. I. Aptekarev, MIAN, M., 2007 , 84 pp.
2006
76.
A. I. Aptekarev, Yu. G. Rykov, “On a variational representation of solutions of a hyperbolic system of equations by means of the logarithmic potential in an external field”, Dokl. Akad. Nauk, 409:1 (2006), 12–14 (cited: 4) (cited: 2)
77.
A. I. Aptekarev, Yu. G. Rykov, “On the variational representation of solutions to some quasilinear equations and systems of hyperbolic type on the basis of potential theory”, Russ. J. Math. Phys., 13:1 (2006), 4–12 (cited: 3) (cited: 5) (cited: 6) (cited: 4)
78.
A. Aptekarev, A. Cachafeiro, F. Marcellán, “A scalar Riemann boundary value problem approach to orthogonal polynomials on the circle”, J. Approx. Theory, 141:2 (2006), 174–181 (cited: 1) (cited: 1)
79.
A. I. Aptekarev, V. Kalyagin, López G. Lagomasino, I. A. Rocha, “On the limit behavior of recurrence coefficients for multiple orthogonal polynomials”, J. Approx. Theory, 139:1-2 (2006), 346–370 (cited: 10) (cited: 12) (cited: 11) (cited: 12)
2005
80.
A. I. Aptekarev, G. López Lagomasino, I. Alvarez Rocha, “Ratio asymptotics of Hermite–Padé polynomials for Nikishin systems”, Sb. Math., 196:8 (2005), 1089–1107 (cited: 21) (cited: 16) (cited: 16) (cited: 16)
81.
A. I. Aptekarev, P. M. Bleher, A. B. J. Kuijlaars, “Large $n$ limit of Gaussian random matrices with external source. II”, Comm. Math. Phys., 259:2 (2005), 367–389 (cited: 67) (cited: 84) (cited: 74) (cited: 76)
2004
82.
A. I. Aptekarev, L. R. Volevich, É. P. Kazandjan, “Numerical method of solving the direct and inverse problems of conformal mappings”, Russ. J. Math. Phys., 11:3 (2004), 277–288 (cited: 1)
83.
A. I. Aptekarev, L. R. Volevich, “Some mathematical aspects of potential flow computation”, Russ. J. Math. Phys., 11:3 (2004), 259–276 (cited: 1)
84.
A. I. Aptekarev, Van W. Assche, “Scalar and matrix Riemann-Hilbert approach to the strong asymptotics of Padé approximants and complex orthogonal polynomials with varying weight”, J. Approx. Theory, 129:2 (2004), 129–166 (cited: 29) (cited: 37) (cited: 38)
85.
M. S. Agranovich, A. I. Aptekarev, N. D. Vvedenskaya, M. I. Vishik, S. G. Gindikin, A. M. Il'in, V. P. Maslov, M. M. Malamud, B. P. Paneah, V. M. Tikhomirov, A. R. Shirikyan, “Leonid Romanovich Volevich (on his 70th birthday)”, Russian Math. Surveys, 59:5 (2004), 991–1000
86.
A. I. Aptekarev, A. L. Afendikov, V. V. Voevodin, et al., “Yulian Borisovich Radvogin”, Russ. J. Math. Phys., 11:3 (2004), 243–249 (cited: 1)
2003
87.
A. I. Aptekarev, A. Branquinho, Van W. Assche, “Multiple orthogonal polynomials for classical weights”, Trans. Amer. Math. Soc., 355:10 (2003), 3887–3914 (electronic) (cited: 61) (cited: 80) (cited: 76)
88.
A. I. Aptekarev, A. Branquinho, “Padé approximants and complex high order Toda lattices”, J. Comput. Appl. Math., 155:2 (2003), 231–237 (cited: 7) (cited: 12) (cited: 11)
2002
89.
A. I. Aptekarev, “Sharp constants for rational approximations of analytic functions”, Sb. Math., 193:1 (2002), 1–72 (cited: 37) (cited: 42) (cited: 26)
90.
A. I. Aptekarev, A. Draux, D. Toulyakov, “Discrete spectra of certain co-recursive Pollaczek polynomials and its applications”, Comput. Methods Funct. Theory, 2:2 (2002), 519–537 (cited: 2)
91.
A. I. Aptekarev, G. T. López Lagomasino, F. Marcellán, “Orthogonal polynomials with respect to a differential operator. Existence and uniqueness”, Conference on Special Functions (Tempe, AZ, 2000), Rocky Mountain J. Math., 32:2 (2002), 467–481 (cited: 4) (cited: 5)
92.
A. I. Aptekarev, M. A. Lapik, “Lagrange Spectrum and Dynamics on the Invariant Sets of Linear-Fractional IFS-s.”, Keldysh Institute preprints, 2002, 43–I
2001
93.
A. I. Aptekarev, Van W. Assche, “Asymptotics of discrete orthogonal polynomials and the continuum limit of the Toda lattice”, Symmetries and integrability of difference equations (Tokyo, 2000), J. Phys. A, 34:48 (2001), 10627–10637 (cited: 7) (cited: 12) (cited: 12)
94.
A. I. Aptekarev, W. Van Assche, “A matrix Riemann-Hilbert problem approach to the strong asymptotics of orthogonal polynomials with respect to a complex weight”, Keldysh Institute preprints, 2001, 27–I
95.
A. I. Aptekarev, W. Van Assche, S. P. Suetin, “A scalar Riemann problem approach to the strong asymptotics of Padé approximates and orthogonal polynomials”, Keldysh Institute preprints, 2001, 26–I
2000
96.
A. I. Aptekarev, A. Draux, V. A. Kalyagin, “On the asymptotics of sharp constants in Markov–Bernstein inequalities in integral metrics with classical weight”, Russian Math. Surveys, 55:1 (2000), 163–165 (cited: 3) (cited: 3)
97.
A. I. Aptekarev, Kastro M. Smirnova, “Convergence of vector Stieltjes continued fractions”, Dokl. Akad. Nauk, 375:6 (2000), 727–729 (cited: 3)
98.
A. Aptekarev, E. Berriochoa, A. Cachafeiro, “On a characterization of integrability for the reciprocal weight of orthogonal polynomials on the circle”, Acta Appl. Math., 61:1-3 (2000), 81–86
99.
A. Aptekarev, V. Kaliaguine, Van J. Iseghem, “The genetic sums' representation for the moments of a system of Stieltjes functions and its application”, Constr. Approx., 16:4 (2000), 487–524 (cited: 30) (cited: 28) (cited: 32)
100.
A. I. Aptekarev, W. Van Assche, A. B. Kuijlaars, “The continuum limit of the Toda lattice and discrete orthogonal polynomials”, Keldysh Institute preprints, 2000, 12–I
1999
101.
A. I. Aptekarev, “Strong asymptotics of multiply orthogonal polynomials for Nikishin systems”, Sb. Math., 190:5 (1999), 631–669 (cited: 23) (cited: 22) (cited: 17)
102.
A. I. Aptekarev, V. A. Kaliaguine, “On a generalization of the nonlinear Langmuir chains”, Self-similar systems (1998, Dubna), Joint Inst. Nuclear Res., Dubna, 1999, 289–294
103.
A. Aptekarev, E. Berriochoa, A. Cachafeiro, “Strong asymptotics for the continuous Sobolev orthogonal polynomials on the unit circle”, J. Approx. Theory, 100:2 (1999), 381–391 (cited: 8) (cited: 8) (cited: 8)
1998
104.
A. I. Aptekarev, “Multiple orthogonal polynomials”, J. Comput. Appl. Math., 99:1-2 (1998), 423–447 (cited: 86) (cited: 101) (cited: 94)
105.
A. Aptekarev, V. Kaliaguine, “Complex rational approximation and difference operators”, Rend. Circ. Mat. Palermo (2) Suppl., I:52 (1998), 3–21 (cited: 8)
106.
J. S. Dehesa, R. J. Yáñez, A. I. Aptekarev, V. Buyarov, “Strong asymptotics of Laguerre polynomials and information entropies of two-dimensional harmonic oscillator and one-dimensional Coulomb potentials”, J. Math. Phys., 39:6 (1998), 3050–3060 (cited: 12) (cited: 57) (cited: 55)
1997
107.
A. I. Aptekarev, F. Marcellán, I. A. Rocha, “Semiclassical multiple orthogonal polynomials and the properties of Jacobi-Bessel polynomials”, J. Approx. Theory, 90:1 (1997), 117–146 (cited: 17) (cited: 21) (cited: 21)
108.
A. I. Aptekarev, A. Branquinho, F. Marcellán, “Toda-type differential equations for the recurrence coefficients of orthogonal polynomials and Freud transformation”, J. Comput. Appl. Math., 78:1 (1997), 139–160 (cited: 14) (cited: 21) (cited: 23)
1996
109.
A. I. Aptekarev, V. S. Buyarov, Van V. Asse, I. S. Degeza, “Asymptotics of entropy integrals for orthogonal polynomials”, Dokl. Akad. Nauk, 346:4 (1996), 439–441 (cited: 2) (cited: 5) (cited: 6) (cited: 7)
110.
S. P. Novikov, A. I. Aptekarev, E. P. Dolzhenko, V. A. Kalyagin, V. V. Kozlov, Yu. V. Nesterenko, M. K. Potapov, V. N. Sorokin, P. L. Ul'yanov, “Evgenii Mikhailovich Nikishin (on the fiftieth anniversary of his birth)”, Russian Math. Surveys, 51:2 (1996), 361–362
1995
111.
A. I. Aptekarev, V. Kaliaguine, Van W. Assche, “Criterion for the resolvent set of nonsymmetric tridiagonal operators”, Proc. Amer. Math. Soc., 123:8 (1995), 2423–2430 (cited: 18) (cited: 24) (cited: 23)
112.
A. I. Aptekarev, V. A. Kalyagin, V. V. Kozlov, M. K. Potapov, V. N. Sorokin, P. L. Ul'yanov, A. T. Fomenko, A. B. Shidlovskiĭ, “Evgeniĭ Mikhaĭlovich Nikishin”, Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1995, no. 6, 110–111 (cited: 1)
113.
A. I. Aptekarev, V. S. Buyarov, I. S. Degeza, “Asymptotic behavior of the $l^P$-norms and the entropy for general orthogonal polynomials”, Russian Acad. Sci. Sb. Math., 82:2 (1995), 373–395 (cited: 50) (cited: 43)
1993
114.
A. I. Aptekarev, “A direct proof for Trefethen's conjecture”, Methods of Approximation Theory in Complex Analysis and Mathematical Physics, May 13–24, 1991, Leningrad, Lecture Notes in Math., 1550, Springer, Berlin, 1993, 147–148 (cited: 1)
115.
A. I. Aptekarev, “Asymptotics of orthogonal polynomials in a neighborhood of the endpoints of the interval of orthogonality”, Russian Acad. Sci. Sb. Math., 76:1 (1993), 35–50 (cited: 9) (cited: 9)
1992
116.
A. I. Aptekarev, H. Stahl, “Asymptotics of Hermite-Padé polynomials”, Progress in approximation theory (1990, Tampa, FL), Springer Ser. Comput. Math., 19, Springer, New York, 1992, 127–167 (cited: 22)
1989
117.
A. I. Aptekarev, “Asymptotics of simultaneously orthogonal polynomials in the Angelesco case”, Math. USSR-Sb., 64:1 (1989), 57–84 (cited: 1) (cited: 5)
1988
118.
A. I. Aptekarev, L. R. Volevich, “The finite element method in a problem of subsonic potential flows of compressible gas around bodies”, Akad. Nauk SSSR Inst. Prikl. Mat. Preprint, 1988, no. 74, 26 (cited: 1)
119.
A. I. Aptekarev, L. R. Volevich, “Calculation of subsonic potential flow around smooth and pointed profiles by means of higher-order finite elements”, Akad. Nauk SSSR Inst. Prikl. Mat. Preprint, 1988, no. 103, 25 (cited: 1)
120.
A. I. Aptekarev, “Asymptotics of orthogonal polynomials with matrix coefficients”, Akad. Nauk SSSR Inst. Prikl. Mat. Preprint, 1988, no. 71, 28 (cited: 1)
121.
A. I. Aptekarev, L. R. Volevich, “Calculation of axially symmetric potential subsonic flows by means of higher-order finite elements”, Akad. Nauk SSSR Inst. Prikl. Mat. Preprint, 1988, no. 101, 27 (cited: 1)
1987
122.
A. I. Aptekarev, “Asymptotic behavior of polynomials of simultaneous orthogonality and of a system of extremal problems for analytic functions”, Akad. Nauk SSSR Inst. Prikl. Mat. Preprint, 1987, no. 168, 29 (cited: 1)
123.
A. I. Aptekarev, V. A. Kalyagin, “Analytic properties of two-dimensional continued $P$-fraction expansions with periodic coefficients and their simultaneous Padé-Hermite approximants”, Rational approximation and applications in mathematics and physics (Łańcut, 1985), Lecture Notes in Math., 1237, Springer, Berlin, 1987, 145–160
124.
A. I. Aptekarev, V. V. Kozlov, A. M. Olevskiĭ, M. K. Potapov, P. L. Ul'yanov, A. B. Shidlovskiĭ, “In memory of Evgeniĭ Mikhaĭlovich Nikishin”, Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1987, no. 6, 88–91 (cited: 1)
1986
125.
A. I. Aptekarev, “Forced motions of a one-sided Langmuir chain”, Theory of functions and approximations, Part 2 (Russian) (Saratov, 1984), Saratov. Gos. Univ., Saratov, 1986, 17–21 (cited: 3)
126.
A. I. Aptekarev, V. A. Kalyagin, “Analytic properties of functions representable by $P^{(m)}$-fractions with periodic coefficients”, Akad. Nauk SSSR Inst. Prikl. Mat. Preprint, 1986, no. 57, 12
127.
A. I. Aptekarev, V. A. Kalyagin, “Asymptotic behavior of an $n$th degree root of polynomials of simultaneous orthogonality, and algebraic functions”, Akad. Nauk SSSR Inst. Prikl. Mat. Preprint, 1986, no. 60, 18 (cited: 5)
1985
128.
A. I. Aptekarev, “Analytic properties of functions represented by two-dimensional continued fractions with constant coefficients and their simultaneous Padé-Hermite approximants (type $II$)”, Akad. Nauk SSSR Inst. Prikl. Mat. Preprint, 1985, no. 79, 12
1986
129.
A. I. Aptekarev, “Asymptotic properties of polynomials orthogonal on a system of contours, and periodic motions of Toda lattices”, Math. USSR-Sb., 53:1 (1986), 233–260 (cited: 53)
1984
130.
A. I. Aptekarev, E. M. Nikishin, “The scattering problem for a discrete Sturm–Liouville operator”, Math. USSR-Sb., 49:2 (1984), 325–355 (cited: 47)
1981
131.
A. I. Aptekarev, “On Padé approximations for the set $\{_{1}F_{1}(1, c; \lambda _{i}z)\}^{k}_{i=1}$”, Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1981, no. 2, 58–62, 88 (cited: 1) (cited: 1)
132.
A. I. Aptekarev, “Convergence of rational approximations to a set of exponential functions”, Vestnik Moskov. Univ. Ser. I Mat. Mekh., 1981, no. 1, 68–74, 108 (cited: 2) (cited: 3)
1982
133.
A. I. Aptekarev, “Asymptotics of Hadamard determinants and the convergence of rows of Padé approximants for sums of exponentials”, Math. USSR-Sb., 41:4 (1982), 427–441 (cited: 1)
134.
A. I. Aptekarev, D. N. Tulyakov, “The Hesse parametrization of a spectral curve”, Mat. Zametki (to appear)
Continuum limits of integrable systems Alexander Aptekarev School-Seminar "Interaction of Mathematics and Physics: New Perspectives" for graduate students and young researchers August 30, 2012 17:00
Complex analysis, mathematical physics, and applications, Collected papers, Tr. Mat. Inst. Steklova, 301, ed. A. I. Aptekarev, M. O. Katanaev, S. P. Suetin, 2018 http://mi.mathnet.ru/book1696
Rational Approximation of Euler's Constant and Recurrence Relations, Collected papers, Sovrem. Probl. Mat., 9, ed. A. I. Aptekarev, 2007, 84 с. http://mi.mathnet.ru/book232
2018
Terms of Use