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Izvestiya: Mathematics, 2018, Volume 82, Issue 1, Pages 186–211
DOI: https://doi.org/10.1070/IM8489 (Mi im8489) 		 
Certain approximation problems for functions on the infinite-dimensional torus: Lipschitz spaces

S. S. Platonov

Petrozavodsk State University, Faculty of Mathematics
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DOI: https://doi.org/10.1070/IM8489
Abstract: We consider some questions about the approximation of functions on the infinite-dimensional torus by trigonometric polynomials. Our main results are analogues of the direct and inverse theorems in the classical theory of approximation of periodic functions and a description of the Lipschitz spaces on the infinite-dimensional torus in terms of the best approximation.
Keywords: Lipschitz spaces, infinite-dimensional torus, harmonic analysis on compact groups, approximation of functions, function spaces.
Received: 12.12.2015
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2018, Volume 82, Issue 1, Pages 198–224
DOI: https://doi.org/10.4213/im8489
Bibliographic databases:
UDC: 517.518.8
MSC: 22E65, 41A17, 41A25, 42A10, 43A75
Language: English
Original paper language: Russian
Citation: S. S. Platonov, “Certain approximation problems for functions on the infinite-dimensional torus: Lipschitz spaces”, Izv. RAN. Ser. Mat., 82:1 (2018), 198–224; Izv. Math., 82:1 (2018), 186–211
Citation in format AMSBIB
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:483
    Russian version PDF:64
    English version PDF:17
    References:67
    First page:37
     
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