Subsequences of the partial sums of a trigonometric series which are everywhere convergent to zero

1963 ◽  
pp. 31-50 ◽  
Author(s):  
N. K. Bari
Keyword(s):  
Trigonometric Series ◽  
Partial Sums

Trigonometric series with nonnegative partial sums

1983 ◽  
Vol 33 (4) ◽  
pp. 287-293
Author(s):  
L. A. Shaginyan
Keyword(s):  
Trigonometric Series ◽  
Partial Sums

Trigonometric series with positive partial sums

1993 ◽  
Vol 53 (3) ◽  
pp. 348-350 ◽  
Author(s):  
V. A. Yudin
Keyword(s):  
Trigonometric Series ◽  
Partial Sums

On a Problem of Littlewood

1996 ◽  
Vol 3 (2) ◽  
pp. 121-132
Author(s):  
M. Khazaradze
Keyword(s):  
Fourier Series ◽  
Trigonometric Series ◽  
Orthogonal Series ◽  
Orthonormal System ◽  
Partial Sums

Abstract The theorem on the tending to zero of coefficients of a trigonometric series is proved when the L 1-norms of partial sums of this series are bounded. It is shown that the analog of Helson's theorem does not hold for orthogonal series with respect to the bounded orthonormal system. Two facts are given that are similar toWeis' theorem on the existence of a trigonometric series which is not a Fourier series and whose L 1-norms of partial sums are bounded.

scholarly journals Integrability and L-convergence of multiple trigonometric series

1994 ◽  
Vol 49 (2) ◽  
pp. 333-339 ◽  
Author(s):  
Chang-Pao Chen
Keyword(s):  
Trigonometric Series ◽  
Partial Sums ◽  
Double Trigonometric Series ◽  
Multiple Trigonometric Series ◽  
Image Position

It is proved that under the following condition, the sum f of the double trigonometric series with coefficients cjk is integrable and the rectangular partial sums smn(f, x, y) converge to f in L1 norm:.

Coefficients of trigonometric series with nonnegative partial sums

1987 ◽  
Vol 41 (2) ◽  
pp. 88-92
Author(s):  
A. S. Belov
Keyword(s):  
Trigonometric Series ◽  
Partial Sums

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

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