ON THE CONVERGENCE OF FOURIER–LAPLACE SERIES

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Submitted: 2025-02-28; Published: 2025-02-28

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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 |||| .