Pointwise Convergence and Summability of Trigonometric Series

1996 ◽  
pp. 35-70
Author(s):  
Levan Zhizhiashvili
Keyword(s):  
Trigonometric Series ◽  
Pointwise Convergence

scholarly journals L1-convergence of double trigonometric series

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3759-3771
Author(s):  
Karanvir Singh ◽  
Kanak Modi
Keyword(s):  
Trigonometric Series ◽  
Bounded Variation ◽  
Pointwise Convergence ◽  
Null Sequence ◽  
Sine Series ◽  
Double Trigonometric Series ◽  
L1 Norm ◽  
Cosine Series

In this paper we study the pointwise convergence and convergence in L1-norm of double trigonometric series whose coefficients form a null sequence of bounded variation of order (p,0),(0,p) and (p,p) with the weight (jk)p-1 for some integer p > 1. The double trigonometric series in this paper represents double cosine series, double sine series and double cosine sine series. Our results extend the results of Young [9], Kolmogorov [4] in the sense of single trigonometric series to double trigonometric series and of M?ricz [6,7] in the sense of higher values of p.

scholarly journals Pointwise Convergence of Trigonometric Series

1987 ◽  
Vol 43 (3) ◽  
pp. 291-300 ◽  
Author(s):  
Chang-Pao Chen
Keyword(s):  
Fourier Series ◽  
Trigonometric Series ◽  
Nonnegative Integer ◽  
Pointwise Convergence ◽  
Convergence Problem ◽  
Hardy’S Theorem ◽  
Fatou’S Theorem

We establish two results in the pointwise convergence problem of a trigonometric series for some nonnegative integer m. These results not only generalize Hardy's theorem, the Jordan test theorem and Fatou's theorem, but also complement the results on pointwise convergence of those Fourier series associated with known L1-convergence classes. A similar result is also established for the case that , where {ln} satisfies certain conditions.

scholarly journals Double trigonometric series with coefficients of bounded variation of higher order

2004 ◽  
Vol 35 (3) ◽  
pp. 267-280 ◽  
Author(s):  
Kulwinder Kaur ◽  
S. S. Bhatia ◽  
Babu Ram
Keyword(s):  
Uniform Convergence ◽  
Trigonometric Series ◽  
Bounded Variation ◽  
Pointwise Convergence ◽  
Higher Order ◽  
Null Sequence ◽  
Partial Sums ◽  
Convergence Properties ◽  
Double Trigonometric Series

In this paper the following convergence properties are established for the rectangular partial sums of the double trigonometric series, whose coefficients form a null sequence of bounded variation of order $ (p,0) $, $ (0,p) $ and $ (p,p) $, for some $ p\ge 1$: (a) pointwise convergence; (b) uniform convergence; (c) $ L^r $-integrability and $ L^r $-metric convergence for $ 0

scholarly journals Pointwise Convergence of Multiple Trigonometric Series

1994 ◽  
Vol 185 (3) ◽  
pp. 629-646 ◽  
Author(s):  
C.P. Chen ◽  
H.C. Wu ◽  
F. Moricz
Keyword(s):  
Trigonometric Series ◽  
Pointwise Convergence ◽  
Multiple Trigonometric Series

Trigonometric series with a given spectrum

2020 ◽  
Vol 2 (4) ◽  
pp. 881-906
Author(s):  
Yves Meyer
Keyword(s):  
Trigonometric Series
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