Some Problems in the Theory of Approximation of Functions on the Group of p-Adic Numbers

被引：3

作者：

Platonov S.S. ^{[1
]}

机构：

[1] Institute ofMathematics, Petrozavodsk State University, Lenina av., 33, Petrozavodsk

来源：

p-Adic Numbers, Ultrametric Analysis and Applications | 2018年 / 10卷 / 2期

关键词：

approximation of functions; embedding theorems; group of p-adic numbers; Lipschitz condition; modulus of continuity; p-adic harmonic analysis; padic Fourier transform;

D O I：

10.1134/S207004661802005X

中图分类号：

学科分类号：

摘要：

Some problems in the theory of approximation of complex-valued functions on the group Qp in the metric of Lρ, 1 ≤ 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. © 2018, Pleiades Publishing, Ltd.

引用

页码：118 / 129

页数：11

共 13 条

[1] An analogue of the Titchmarsh theorem for the Fourier transform on the group of p-adic numbers
Platonov S.S.
p-Adic Numbers, Ultrametric Analysis and Applications, 2017, 9 (2) : 158 - 164
[2] On a characterization theorem for the group of p-adic numbers
Feldman, Gennadiy
PUBLICATIONES MATHEMATICAE-DEBRECEN, 2015, 87 (1-2): : 147 - 166
[3] On the Skitovich-Darmois Theorem for the Group of p-Adic Numbers
Feldman, Gennadiy
JOURNAL OF THEORETICAL PROBABILITY, 2015, 28 (02) : 539 - 549
[4] Some Problems in the Theory of Approximation of Functions on Locally Compact Vilenkin Groups
Sergey S. Platonov
p-Adic Numbers, Ultrametric Analysis and Applications, 2019, 11 : 163 - 175
[5] Some Problems in the Theory of Approximation of Functions on Locally Compact Vilenkin Groups
Platonov, Sergey S.
P-ADIC NUMBERS ULTRAMETRIC ANALYSIS AND APPLICATIONS, 2019, 11 (02) : 163 - 175
[6] GREEN FUNCTIONS ON THE P-ADIC VECTOR SPACE
Son, Jin-Woo
Rim, Kyung Soo
COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2005, 20 (04): : 657 - 669
[7] Some problems in the theory of approximation of functions on compact homogeneous manifolds
Platonov, S. S.
SBORNIK MATHEMATICS, 2009, 200 (5-6) : 845 - 885
[8] A Distributional Proof of p-Adic Wiener Tauberian Theorem and Approximation by Translates of a Function
Volosivets, S. S.
P-ADIC NUMBERS ULTRAMETRIC ANALYSIS AND APPLICATIONS, 2021, 13 (04) : 308 - 315
[9] On some extremal problems of approximation theory of functions on the real axis I
Vakarchuk S.B.
Journal of Mathematical Sciences, 2013, 188 (2) : 146 - 166
[10] Bessel generalized translations and some problems of approximation theory for functions on the half-line
S. S. Platonov
Siberian Mathematical Journal, 2009, 50 : 123 - 140

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