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On the best approximations of functions defined on zero-dimensional groups

Autor: M. F. Timan

Publikováno v: Ukrainian Mathematical Journal. 64:823-834

We present a survey of results obtained by the author, his disciples, and other mathematicians and related to the problem of finding the best approximations of functions in the investigation of properties of spaces of functions defined on zero-dimens

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::072366de32ab27c21df1e893de66aece
https://doi.org/10.1007/s11253-012-0681-6

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Approximations of almost periodic functions by entire ones

Autor: M. F. Timan, Yu. Kh. Khasanov

Publikováno v: Russian Mathematics. 55:52-57

In this paper we propose a new proof of the well-known theorem by S. N. Bernstein, according to which among entire functions which give on (−∞,∞) the best uniform approximation of order σ of periodic functions there exists a trigonometric poly

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::41364a55976a8a3bcdd32dabb2fe00ab
https://doi.org/10.3103/s1066369x11120085

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On the absolute summability of Fourier series of almost-periodic besicovitch functions

Autor: Yu. Kh. Khasanov, M. F. Timan

Publikováno v: Ukrainian Mathematical Journal. 61:1499-1510

For almost-periodic Besicovitch functions whose spectrum has a limit point only at infinity, we establish criteria for the absolute Cesaro summability of their Fourier series of order greater than -1.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::a889f772ccb2c2a2de804ff0cd45b3d7
https://doi.org/10.1007/s11253-010-0292-z

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On some inequalities for polynomials

Autor: M. F. Timan

Publikováno v: Ukrainian Mathematical Journal. 50:1473-1477

We prove the equivalence between analogs of the Paley and Nikol’skii inequalities for any orthonormal system of functions and for almost periodic polynomials with arbitrary spectrum.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::a3e3271b813528935674d9b21b7ff730
https://doi.org/10.1007/bf02525256

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On uniform approximations of almost periodic functions by entire functions of finite degree

Autor: M. F. Timan

Publikováno v: Ukrainian Mathematical Journal. 47:1449-1454

We give a new proof of the well-known Bernshtein statement that, among entire functions of degree ≤σ which realize the best uniform approximation (of degree σ) of a periodic function on (−∞,∞), there is a trigonometric polynomial of degree

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::be5b82c5db9e43ef08d87dedad03ab06
https://doi.org/10.1007/bf01057520

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