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Izv. RAN. Ser. Mat., 2018, Volume 82, Issue 1, Pages 198–224 (Mi izv8489)  

Certain approximation problems for functions on the infinite-dimensional torus: Lipschitz spaces

S. S. Platonov

Petrozavodsk State University, Faculty of Mathematics

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.

DOI: https://doi.org/10.4213/im8489

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English version:
Izvestiya: Mathematics, 2018, 82:1, 186–211

Bibliographic databases:

UDC: 517.518.8
MSC: 22E65, 41A17, 41A25, 42A10, 43A75
Received: 12.12.2015

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

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  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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