scholarly journals On uniform convergence of one class of double trigonometric series

2021 ◽  
pp. 47
Author(s):  
M.I. Alkhimov
Keyword(s):  
Uniform Convergence ◽  
Trigonometric Series ◽  
Sufficient Conditions ◽  
Fixed Number ◽  
Double Trigonometric Series

We have established sufficient conditions of uniform convergence of the series of the form $\sum\limits_{k,l=1} a_{k,l} \sin kx \sin ly$ in the strip: $-\infty < x < +\infty$, $\delta \leqslant y \leqslant 2\pi - \delta$ ($\delta$ is a fixed number, $0 < \delta < \pi$).

scholarly journals Norm inequalities in multidimensional Lorentz spaces

2008 ◽  
Vol 103 (2) ◽  
pp. 278
Author(s):  
Boris Simonov ◽  
Sergey Tikhonov
Keyword(s):  
Trigonometric Series ◽  
Sufficient Conditions ◽  
Lorentz Spaces ◽  
Necessary And Sufficient Conditions ◽  
Double Trigonometric Series ◽  
Norm Inequalities ◽  
Necessary And Sufficient

In this paper we obtain necessary and sufficient conditions for double trigonometric series to belong to generalized Lorentz spaces, not symmetric in general. Estimates for the norms are given in terms of coefficients.

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

Uniform Convergence of Trigonometric Series with General Monotone Coefficients

2019 ◽  
Vol 71 (6) ◽  
pp. 1445-1463
Author(s):  
Mikhail Dyachenko ◽  
Askhat Mukanov ◽  
Sergey Tikhonov
Keyword(s):  
Uniform Convergence ◽  
Rate Of Convergence ◽  
Trigonometric Series ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Monotone Coefficients ◽  
Fourier Sums ◽  
Necessary And Sufficient

AbstractWe study criteria for the uniform convergence of trigonometric series with general monotone coefficients. We also obtain necessary and sufficient conditions for a given rate of convergence of partial Fourier sums of such series.

scholarly journals Limit of 𝑝-Laplacian obstacle problems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Raffaela Capitanelli ◽  
Maria Agostina Vivaldi
Keyword(s):  
Asymptotic Behavior ◽  
Uniform Convergence ◽  
Explicit Expression ◽  
Positive Measure ◽  
Sufficient Conditions ◽  
Obstacle Problems ◽  
Dimensional Case ◽  
Asymptotic Behavior Of Solutions ◽  
One Dimensional ◽  
The One

AbstractIn this paper, we study asymptotic behavior of solutions to obstacle problems for p-Laplacians as {p\to\infty}. For the one-dimensional case and for the radial case, we give an explicit expression of the limit. In the n-dimensional case, we provide sufficient conditions to assure the uniform convergence of the whole family of the solutions of obstacle problems either for data f that change sign in Ω or for data f (that do not change sign in Ω) possibly vanishing in a set of positive measure.

Completeness of the L1-space of closed vector measures

1990 ◽  
Vol 33 (1) ◽  
pp. 71-78 ◽  
Author(s):  
Werner J. Ricker
Keyword(s):  
Uniform Convergence ◽  
Convex Space ◽  
Vector Measure ◽  
Sufficient Conditions ◽  
Locally Convex Space ◽  
Vector Measures ◽  
Locally Convex

The notion of a closed vector measure m, due to I. Kluv´;nek, is by now well established. Its importance stems from the fact that if the locally convex space X in which m assumes its values is sequentially complete, then m is closed if and only if its L1-space is complete for the topology of uniform convergence of indefinite integrals. However, there are important examples of X-valued measures where X is not sequentially complete. Sufficient conditions guaranteeing the completeness of L1(m) for closed X-valued measures m are presented without the requirement that X be sequentially complete.

Sign in / Sign up

Export Citation Format

Share Document