2009; Physical and Mathematical Sciences, 43(1 (218): 3–7
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ON THE CONVERGENCE OF FOURIER–LAPLACE SERIES

A. S. Sargsyan*

Received: 2025-02-28 · Published: 2009-02-19

© 2009 The Author(s) and the original publisher.

CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
ON THE CONVERGENCE OF FOURIER–LAPLACE SERIES
Author
A. S. Sargsyan
Published
2009-02-19
Licence
Creative Commons Attribution 4.0 International

Abstract

In the present paper we prove the following theorem.For any 0>ε there exists a measurable set 3⊂GS with measure mes4>−Gπε, such that for each 13()( )∈fxLS there is a function 13()( )∈gxLS, coinciding with ()fx on G with the following properties. Its Fourier–Laplace series converges to g(x) in metrics L1(S3) and the inequality holds 1313()1()sup[ , ( , )]312 |||| .
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