Summability of Fourier-Laplace Series with the Method of Lacunary Arithmetical Means at Lebesgue Points

2001 ◽  
Vol 17 (3) ◽  
pp. 489-496
Author(s):  
Feng Dai ◽  
Kun Yang Wang
Keyword(s):  
Laplace Series ◽  
Lebesgue Points

scholarly journals Lebesgue points of $$\ell _1$$-Cesàro summability of d-dimensional Fourier series

2021 ◽  
Vol 6 (3) ◽  
Author(s):  
Ferenc Weisz
Keyword(s):  
Fourier Series ◽  
Lebesgue Point ◽  
Cesàro Means ◽  
Cesàro Summability ◽  
Cesaro Means ◽  
Cesaro Summability ◽  
Lebesgue Points ◽  
Cesáro Means

AbstractWe generalize the classical Lebesgue’s theorem and prove that the $$\ell _1$$ ℓ 1 -Cesàro means of the Fourier series of the multi-dimensional function $$f\in L_1({{\mathbb {T}}}^d)$$ f ∈ L 1 ( T d ) converge to f at each strong $$\omega $$ ω -Lebesgue point.

scholarly journals On the Lebesgue constants of Fourier-Laplace series by Riesz Means

2017 ◽  
Vol 819 ◽  
pp. 012018
Author(s):  
Ahmad Fadly Nurullah bin Rasedee ◽  
Abdumalik A. Rakhimov ◽  
Anvarjon A. Ahmedov ◽  
Torla Bin Hj Hassan
Keyword(s):  
Lebesgue Constants ◽  
Riesz Means ◽  
Laplace Series

scholarly journals Fine properties of the subdifferential for a class of one-homogeneous functionals

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Antonin Chambolle ◽  
Michael Goldman ◽  
Matteo Novaga
Keyword(s):  
Total Variation ◽  
Lebesgue Points

AbstractWe collect some known results on the subdifferentials of a class of one-homogeneous functionals, which consist in anisotropic and nonhomogeneous variants of the total variation. It is known that the subdifferential at a point is the divergence of some “calibrating field”. We establish new relationships between Lebesgue points of a calibrating field and regular points of the level surfaces of the corresponding calibrated function.

scholarly journals Convergence rate of Fourier–Laplace series of L2-functions

2004 ◽  
Vol 128 (2) ◽  
pp. 103-114 ◽  
Author(s):  
Chin-Cheng Lin ◽  
Kunyang Wang
Keyword(s):  
Convergence Rate ◽  
Laplace Series
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