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Uspekhi Mat. Nauk, 1996, Volume 51, Issue 6(312), Pages 89–124 (Mi umn1019)  

This article is cited in 68 scientific papers (total in 68 papers)

Approximation of unbounded operators by bounded operators and related extremal problems

V. V. Arestov

Ural State University


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English version:
Russian Mathematical Surveys, 1996, 51:6, 1093–1126

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UDC: 517.518+517.983
MSC: 41A50, 47A52
Received: 12.09.1996

Citation: V. V. Arestov, “Approximation of unbounded operators by bounded operators and related extremal problems”, Uspekhi Mat. Nauk, 51:6(312) (1996), 89–124; Russian Math. Surveys, 51:6 (1996), 1093–1126

Citation in format AMSBIB
\by V.~V.~Arestov
\paper Approximation of unbounded operators by bounded operators and related extremal problems
\jour Uspekhi Mat. Nauk
\yr 1996
\vol 51
\issue 6(312)
\pages 89--124
\jour Russian Math. Surveys
\yr 1996
\vol 51
\issue 6
\pages 1093--1126

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    This publication is cited in the following articles:
    1. G. G. Magaril-Il'yaev, V. M. Tikhomirov, “Kolmogorov-type inequalities for derivatives”, Sb. Math., 188:12 (1997), 1799–1832  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. A. Ilyin, “Best constants in a class of polymultiplicative inequalities for derivatives”, Sb. Math., 189:9 (1998), 1335–1359  mathnet  crossref  crossref  mathscinet  isi  elib
    3. V. V. Arestov, “The best approximation to a class of functions of several variables by another class and related extremum problems”, Math. Notes, 64:3 (1998), 279–294  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. S. N. Kudryavtsev, “The Stechkin problem for partial derivation operators on classes of finitely smooth functions”, Math. Notes, 67:1 (2000), 61–68  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. Timonov A., “Factorised preconditionings of successive approximations in finite precision”, BIT, 41:3 (2001), 582–598  crossref  mathscinet  zmath  isi  scopus  scopus
    6. Michael V Klibanov, Alexandre Timonov, “A sequential minimization algorithm based on the convexification approach”, Inverse Probl, 19:2 (2003), 331  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    7. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Optimal Recovery of Functions and Their Derivatives from Inaccurate Information about the Spectrum and Inequalities for Derivatives”, Funct. Anal. Appl., 37:3 (2003), 203–214  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. G. G. Skorik, “On the best error estimate for the method of averaging kernels in the problem of the differentiation of a noisy function”, Russian Math. (Iz. VUZ), 48:3 (2004), 70–74  mathnet  mathscinet  zmath  elib
    9. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “Optimal recovery of values of functions and their derivatives from inaccurate data on the Fourier transform”, Sb. Math., 195:10 (2004), 1461–1476  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. R. R. Akopian, “Kolmogorov's inequality for functions analytic in a half-plane”, Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 2, S1–S8  mathnet  mathscinet  zmath  elib
    11. Timonov, A, “A new iterative procedure for the numerical solution of coefficient inverse problems”, Applied Numerical Mathematics, 54:2 (2005), 280  crossref  mathscinet  zmath  isi  scopus  scopus
    12. G. G. Skorik, “An error estimate for the method of mean functions in the problem of the numerical differentiation of a noisy function”, Russian Math. (Iz. VUZ), 50:2 (2006), 33–39  mathnet  mathscinet  zmath
    13. Adrian Nachman, Alexandru Tamasan, Alexandre Timonov, “Conductivity imaging with a single measurement of boundary and interior data”, Inverse Probl, 23:6 (2007), 2551  crossref  mathscinet  zmath  isi  scopus  scopus
    14. A. Timonov, M. V. Klibanov, “A globally convergent convexification algorithm for multidimensional coefficient inverse problems”, j inv ill-posed problems, 15:2 (2007), 167  crossref  mathscinet  zmath  scopus  scopus
    15. S. N. Kudryavtsev, “Approximation and reconstruction of the derivatives of functions satisfying mixed Hölder conditions”, Izv. Math., 71:5 (2007), 895–938  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    16. Babenko, VF, “KOLMOGOROV TYPE INEQUALITIES FOR HYPERSINGULAR INTEGRALS WITH HOMOGENEOUS CHARACTERISTIC”, Banach Journal of Mathematical Analysis, 1:1 (2007), 66  crossref  mathscinet  zmath  isi  scopus  scopus
    17. Babenko, VF, “ON KOLMOGOROV-TYPE INEQUALITIES FOR FRACTIONAL DERIVATIVES OF FUNCTIONS OF TWO VARIABLES”, Ukrainian Mathematical Journal, 60:6 (2008), 977  crossref  mathscinet  zmath  isi  scopus  scopus
    18. A. V. Gasnikov, “Time-asymptotic behaviour of a solution of the Cauchy initial-value problem for a conservation law with non-linear divergent viscosity”, Izv. Math., 73:6 (2009), 1111–1148  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    19. Babenko, VF, “Approximation of unbounded operators by bounded operators in a Hilbert space”, Ukrainian Mathematical Journal, 61:2 (2009), 179  crossref  mathscinet  zmath  isi  scopus  scopus
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    23. A. A. Koshelev, “The best approximation of Laplace operator by linear bounded operators in the space $L_p$”, Russian Math. (Iz. VUZ), 55:6 (2011), 53–63  mathnet  crossref  mathscinet  elib
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