Basic Fourier Series: Convergence on and Outside the q-Linear Grid

被引：14

作者：

Cardoso, J. L. ^{[1
]}

机构：

[1] CM UTAD, UTAD, Dept Matemat, P-5001911 Vila Real, Portugal

来源：

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2011年 / 17卷 / 01期

关键词：

q-trigonometric functions; q-Fourier series; Basic Fourier expansions; Uniform convergence; q-linear grid; ZEROS;

D O I：

10.1007/s00041-010-9161-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A q-type Holder condition on a function f is given in order to establish (uniform) convergence of the corresponding basic Fourier series S-q[f] to the function itself, on the set of points of the q-linear grid. Furthermore, by adding other conditions, one guarantees the (uniform) convergence of S-q[f] to f on and "outside" the set points of the q-linear grid.

引用

页码：96 / 114

页数：19

共 47 条

[1] Basic Fourier Series: Convergence on and Outside the q-Linear Grid
J. L. Cardoso
Journal of Fourier Analysis and Applications, 2011, 17 : 96 - 114
[2] Uniform convergence of basic Fourier-Bessel series on a q-linear grid
Abreu, L. D.
Alvarez-Nodarse, R.
Cardoso, J. L.
RAMANUJAN JOURNAL, 2019, 49 (02) : 421 - 449
[3] Basic Fourier series on a q-linear grid:: Convergence theorems
Cardoso, J. L.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 323 (01) : 313 - 330
[4] Uniform convergence of basic Fourier–Bessel series on a q-linear grid
L. D. Abreu
R. Álvarez-Nodarse
J. L. Cardoso
The Ramanujan Journal, 2019, 49 : 421 - 449
[5] Convergence of mock Fourier series
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Journal d’Analyse Mathématique, 2006, 99 : 333 - 353
[6] Uniform convergence of Fourier-Jacobi series
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JOURNAL OF APPROXIMATION THEORY, 2002, 117 (02) : 207 - 228
[7] On the uniform convergence of Walsh-Fourier series
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ACTA MATHEMATICA HUNGARICA, 2001, 93 (1-2) : 59 - 70
[8] On the Uniform Convergence of Walsh-Fourier Series
U. Goginava
Acta Mathematica Hungarica, 2001, 93 : 59 - 70
[9] ON BEHAVIOR OF FOURIER COEFFICIENTS AND UNIFORM CONVERGENCE OF FOURIER SERIES IN THE HAAR SYSTEM
Grigoryan, M. G.
Kobelyan, A. Kh
ADVANCES IN OPERATOR THEORY, 2018, 3 (04): : 781 - 793
[10] On Uniform Convergence of Transformations of Fourier Series on Multiplicative Systems
Agafonova, N. Y.
IZVESTIYA SARATOVSKOGO UNIVERSITETA NOVAYA SERIYA-MATEMATIKA MEKHANIKA INFORMATIKA, 2009, 9 (01): : 3 - 8

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