Abstract:
Order-sharp estimates are established for the best N-term approximations of functions from Nikol'skii–Besov type classes Bsmpq(Tk) with respect to the multiple trigonometric system T(k) in the metric of Lr(Tk) for a number of relations between the parameters s,p,q,r, and m (s=(s1,…,sn)∈Rn+, 1≤p,q,r≤∞, m=(m1,…,mn)∈Nn, k=m1+⋯+mn). Constructive methods of nonlinear trigonometric approximation –variants of the so-called greedy algorithms – are used in the proofs of upper estimates.
Citation:
D. B. Bazarkhanov, “Nonlinear trigonometric approximations of multivariate function classes”, Function spaces, approximation theory, and related problems of mathematical analysis, Collected papers. In commemoration of the 110th anniversary of Academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 293, MAIK Nauka/Interperiodica, Moscow, 2016, 8–42; Proc. Steklov Inst. Math., 293 (2016), 2–36
\Bibitem{Baz16}
\by D.~B.~Bazarkhanov
\paper Nonlinear trigonometric approximations of multivariate function classes
\inbook Function spaces, approximation theory, and related problems of mathematical analysis
\bookinfo Collected papers. In commemoration of the 110th anniversary of Academician Sergei Mikhailovich Nikol'skii
\serial Trudy Mat. Inst. Steklova
\yr 2016
\vol 293
\pages 8--42
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\jour Proc. Steklov Inst. Math.
\yr 2016
\vol 293
\pages 2--36
\crossref{https://doi.org/10.1134/S0081543816040027}
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Linking options:
https://www.mathnet.ru/eng/tm3702
https://doi.org/10.1134/S0371968516020023
https://www.mathnet.ru/eng/tm/v293/p8
This publication is cited in the following 9 articles:
G. Akishev, “Estimates of $M$–term approximations of functions of several variables in the Lorentz space by a constructive method”, Eurasian Math. J., 15:2 (2024), 8–32
G. A. Akishev, “On estimates for orders of best $M$-term approximations
of multivariate functions in anisotropic Lorentz–Karamata spaces”, Ufa Math. J., 15:1 (2023), 1–20
G. A. Akishev, “O poryadkakh $n$-chlennykh priblizhenii funktsii mnogikh peremennykh v prostranstve Lorentsa”, Materialy Voronezhskoi mezhdunarodnoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy», Voronezh, 27 yanvarya — 1 fevralya 2023 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 227, VINITI RAN, M., 2023, 3–19
V. K. Nguyen, V. D. Nguyen, “Best n-Term Approximation of Diagonal Operators and Application to Function Spaces with Mixed Smoothness”, Anal Math, 48:4 (2022), 1127
G. Akishev, A. Myrzagaliyeva, “ON ESTIMATES OF M-TERM APPROXIMATIONS ON CLASSES OF FUNCTIONS WITH BOUNDED MIXED DERIVATIVE IN THE LORENTZ SPACE”, J Math Sci, 266:6 (2022), 870
S. A. Stasyuk, “Razrezhennoe trigonometricheskoe priblizhenie klassov Besova funktsii s maloi smeshannoi gladkostyu”, Tr. IMM UrO RAN, 23, no. 3, 2017, 244–252
D. B. Bazarkhanov, “Sparse approximation of some function classes with respect to multiple Haar system on the unit cube”, International Conference Functional Analysis In Interdisciplinary Applications (FAIA 2017), AIP Conf. Proc., 1880, eds. T. Kalmenov, M. Sadybekov, Amer. Inst. Phys., 2017, UNSP 030017
S. A. Stasyuk, “Konstruktivnye razrezhennye trigonometricheskie priblizheniya dlya klassov funktsii s nebolshoi smeshannoi gladkostyu”, Tr. IMM UrO RAN, 22, no. 4, 2016, 247–253
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