Multiplier Theorem for Fourier Series in continuous-discrete Sobolev orthogonal polynomials

2020/11/28 by Б. П. Осиленкер, Osilenker, B. P.
Mathematics · #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2012.00550

openalex publication_date 2020/11/28 · openalex created_date 2020/12/07 · openalex updated_date 2026/07/28

Abstract

In the paper we study the multipliers of Fourier series in polynomials orthogonal in continuous-discrete Sobolev's spaces. Multiplier Theorem for Fourier-Sobolev series is obtained. This result is based on the representation of the Fejér kernel, on the construction of the "humpbacked majorant" and weighted estimates of maximal functions.

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