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Badkov, Vladimir Mihailovich
(1940–2013)

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Total publications: 26
Scientific articles: 26

Number of views:
This page:961
Abstract pages:5991
Full texts:1809
References:397
Professor
Doctor of physico-mathematical sciences (1996)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 16.05.1940
Keywords: polynomials orthogonal on a segment; polynomials orthogonal on a circle; trigonometric polynomials orthogonal with respect to a weight; weights with non-classical singularities; asymptotic and approximation properties of orthogonal polynomials; the best approximations of the Szeg\ddot{o} function; weight analogs of Markov, Bernstein and Jackson–Nikol'skii inequalities.

Subject:

Uniform asymptotic representations on all range of orthogonality for generalized Jacobi polynomials orthogonal on a circle or a segment and also for trigonometric are obtained. Some questions on (uniform, mean and almost everywhere) convergence of Fourier series with respect to the mentioned polynomials are investigated. Two-sided point-wise estimations (sometimes uniform asymptotic representations) in terms of the Szego function for polynomials orthonormal on a circle (and their derivatives) with respect to a weight (introduced by the author), which orders of singularities are defined by finite products of real powers of concave moduli of continuity. In some cases orders of the best approximations (by algebraic polynomials) of the corresponding Szego function are found.

Biography

Graduated from Faculty of Mathematics and Mechanics of I. I. Mechnikov Odessa State University in 1962 (department of differential equations). Ph.D. thesis was defended in 1969. D.Sci. thesis was defended in 1995. A list of my works contains more than 60 titles.

   
Main publications:
  • Badkov V. M. Approksimativnye svoistva ryadov Fure po ortogonalnym polinomam // UMN, 1978, 33 (4), 51–106.
  • Badkov V. M. Priblizhenie funktsii v ravnomernoi metrike summami Fure po ortogonalnym polinomam // Trudy MIAN, 1980, 145, 20–62.
  • Badkov V. M. Ravnomernye asimptoticheskie predstavleniya ortogonalnykh polinomov // Trudy MIAN, 1983, 164, 3–36.
  • Badkov V. M. Asimptoticheskie i ekstremalnye svoistva ortogonalnykh polinomov // Trudy MIRAN, 1992, 198, 41–88.
  • Badkov V. M. Potochechnye otsenki snizu modulei proizvodnykh mnogochlena, ortogonalnogo na okruzhnosti s vesom, imeyuschim osobennosti // Matem. sbornik, 1995, 186 (6), 3–14.

http://www.mathnet.ru/eng/person8321
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/199205

Publications in Math-Net.Ru
2013
1. V. M. Badkov, “Asymptotic properties of zeros of orthogonal trigonometric polynomials of half-integer orders”, Trudy Inst. Mat. i Mekh. UrO RAN, 19:2 (2013),  54–70  mathnet  mathscinet  elib
2012
2. V. M. Badkov, “Asymptotic formulae for the zeros of orthogonal polynomials”, Mat. Sb., 203:9 (2012),  3–14  mathnet  mathscinet  zmath  elib; Sb. Math., 203:9 (2012), 1231–1243  isi  scopus
3. V. M. Badkov, “Trigonometric analogs of the Szegő equiconvergence theorem for Fourier–Jacobi series”, Trudy Inst. Mat. i Mekh. UrO RAN, 18:4 (2012),  68–79  mathnet  elib
2011
4. V. M. Badkov, “Estimates of the Lebesgue function of Fourier sums over trigonometric polynomials orthogonal with a weight not belonging to the spaces $L^r$ $(r>1)$”, Trudy Inst. Mat. i Mekh. UrO RAN, 17:3 (2011),  71–82  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 277, suppl. 1 (2012), 21–32  isi  scopus
2010
5. V. M. Badkov, “Some properties of Jacobi polynomials orthogonal on a circle”, Trudy Inst. Mat. i Mekh. UrO RAN, 16:4 (2010),  65–73  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S49–S58  isi  scopus
2009
6. V. M. Badkov, “Pointwise estimates of polynomials orthogonal on a circle with respect to a weight not belonging to the spaces $L^r$ ($r>1$).”, Trudy Inst. Mat. i Mekh. UrO RAN, 15:1 (2009),  66–78  mathnet  mathscinet  elib; Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S64–S77  isi
2008
7. V. M. Badkov, “Asymptotic behavior of the maximal zero of a polynomial orthogonal on a segment with a nonclassical weight”, Trudy Inst. Mat. i Mekh. UrO RAN, 14:3 (2008),  38–42  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 264, suppl. 1 (2009), S39–S43  isi  scopus
2005
8. V. M. Badkov, “Zeros of orthogonal polynomials”, Trudy Inst. Mat. i Mekh. UrO RAN, 11:2 (2005),  30–46  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 2, S30–S48
2001
9. V. M. Badkov, “Orders of the weighted Lebesgue constants for Fourier sums with respect to orthogonal polynomials”, Trudy Inst. Mat. i Mekh. UrO RAN, 7:1 (2001),  47–61  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math. (Suppl.), 2001no. , suppl. 1, S48–S64
1998
10. V. M. Badkov, “Maclaurin's expansion of Szegö's function whose weight is positive and satisfies Dini's condition, uniformly converges in the closed disc”, Trudy Inst. Mat. i Mekh. UrO RAN, 5 (1998),  199–204  mathnet  zmath
1995
11. V. M. Badkov, “Pointwise estimates from below of the moduli of the derivatives of orthogonal polynomials on of the derivatives of orthogonal polynomials on”, Mat. Sb., 186:6 (1995),  3–14  mathnet  mathscinet  zmath; Sb. Math., 186:6 (1995), 771–781  isi
1992
12. V. M. Badkov, “Asymptotics of the second kind polynomials and above and below point estimates of its derivatives”, Trudy Inst. Mat. i Mekh. UrO RAN, 1 (1992),  71–83  mathnet  mathscinet  zmath  elib
13. V. M. Badkov, “Asymptotic and extremal properties of orthogonal polynomials corresponding to weight having singularities”, Trudy Mat. Inst. Steklov., 198 (1992),  41–88  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 198 (1994), 37–82
1987
14. V. M. Badkov, “Systems of orthogonal polynomials explicitly represented by the Jacobi polynomials”, Mat. Zametki, 42:5 (1987),  650–659  mathnet  mathscinet  zmath; Math. Notes, 42:5 (1987), 858–863  isi
15. V. M. Badkov, “Uniform asymptotic representations of orthogonal polynomials and their derivatives”, Trudy Mat. Inst. Steklov., 180 (1987),  36–38  mathnet  zmath; Proc. Steklov Inst. Math., 180 (1989), 39–41
1983
16. V. M. Badkov, “Uniform asymptotic representations of orthogonal polynomials”, Trudy Mat. Inst. Steklov., 164 (1983),  6–36  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 164 (1985), 5–41
1980
17. V. M. Badkov, “Approximation of functions in a uniform metric by Fourier sums in orthogonal polynomials”, Trudy Mat. Inst. Steklov., 145 (1980),  20–62  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 145 (1981), 19–65
1979
18. V. M. Badkov, “The asymptotic behavior of orthogonal polynomials”, Mat. Sb. (N.S.), 109(151):1(5) (1979),  46–59  mathnet  mathscinet  zmath; Math. USSR-Sb., 37:1 (1980), 39–51  isi
1978
19. V. M. Badkov, “Approximation properties of Fourier series in orthogonal polynomials”, Uspekhi Mat. Nauk, 33:4(202) (1978),  51–106  mathnet  mathscinet  zmath; Russian Math. Surveys, 33:4 (1978), 53–117
1974
20. V. M. Badkov, “Convergence in the mean and almost everywhere of Fourier series in polynomials orthogonal on an interval”, Mat. Sb. (N.S.), 95(137):2(10) (1974),  229–262  mathnet  mathscinet  zmath; Math. USSR-Sb., 24:2 (1974), 223–256
1973
21. V. M. Badkov, “Convergence in the mean of the Fourier series in orthogonal polynomials”, Mat. Zametki, 14:2 (1973),  161–172  mathnet  mathscinet  zmath; Math. Notes, 14:2 (1973), 651–657
22. V. M. Badkov, “Boundedness in the mean of orthonormalized polynomials”, Mat. Zametki, 13:5 (1973),  759–770  mathnet  mathscinet  zmath; Math. Notes, 13:5 (1973), 453–459
1970
23. V. M. Badkov, “Approximation of functions by partial sums of Fourier series in polynomials orthogonal on an interval”, Mat. Zametki, 8:4 (1970),  431–441  mathnet  mathscinet  zmath; Math. Notes, 8:4 (1970), 712–717
1969
24. V. M. Badkov, “The uniform convergence of fourier series in orthogonal polynomials”, Mat. Zametki, 5:3 (1969),  285–295  mathnet  mathscinet  zmath; Math. Notes, 5:3 (1969), 174–179
1968
25. V. M. Badkov, “Approximation of functions by partial sums of a Fourier series of generalized Jacobi polynomials”, Mat. Zametki, 3:6 (1968),  671–682  mathnet  mathscinet  zmath; Math. Notes, 3:6 (1968), 428–435
1966
26. V. M. Badkov, “Approximation of functions by the Fourier–Jacobi sums”, Dokl. Akad. Nauk SSSR, 167:4 (1966),  731–734  mathnet  mathscinet  zmath

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