Some Problems in the Theory of Approximation of Functions on Locally Compact Vilenkin Groups

被引：4

作者：

Platonov, Sergey S. ^{[1
]}

机构：

[1] Petrozavodsk State Univ, Inst Math, Lenina Av 33, Petrozavodsk 185910, Russia

来源：

P-ADIC NUMBERS ULTRAMETRIC ANALYSIS AND APPLICATIONS | 2019年 / 11卷 / 02期

关键词：

locally compact Vilenkin groups; approximation of functions; modulus of continuity; zero-dimensional groups; Lipschitz condition; embedding theorems; CONTINUITY;

D O I：

10.1134/S2070046619020067

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Some problems in the theory of approximation of complex-valued functions on locally compact Vilenkin groups in the metric of L-p, 1 <= p <= infinity, by functions with bounded spectrum, are investigated. A description of certain function spaces in terms of the best approximations are obtained and some imbedding theorems are proved.

引用

页码：163 / 175

页数：13

共 47 条

[1] Some Problems in the Theory of Approximation of Functions on Locally Compact Vilenkin Groups
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p-Adic Numbers, Ultrametric Analysis and Applications, 2019, 11 : 163 - 175
[2] Fourier Transform of Dini-Lipschitz Functions on Locally Compact Vilenkin Groups
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[3] Fourier Transform of Dini-Lipschitz Functions on Locally Compact Vilenkin Groups
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[4] Some problems in the theory of approximation of functions on compact homogeneous manifolds
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[6] An analogue of the Titchmarsh theorem for the Fourier transform on locally compact Vilenkin groups
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[7] On some extremal problems of approximation theory of functions on the real axis I
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[8] Calderon-Zygmund Operators on Morrey and Hardy-Morrey Spaces in Locally Compact Vilenkin Groups
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[9] Calderón-Zygmund Operators on Morrey and Hardy-Morrey Spaces in Locally Compact Vilenkin Groups
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[10] Bessel generalized translations and some problems of approximation theory for functions on the half-line
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