Notes on the Overconvergence of Fourier Series and Hadamard–Ostrowski Gaps-Reference-Cited by-同舟云学术

Notes on the Overconvergence of Fourier Series and Hadamard–Ostrowski Gaps

Published:2024-03-25 Issue:7 Volume:12 Page:979
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Stoenchev Miroslav¹,Todorov Venelin²³^ORCID,Georgiev Slavi²⁴^ORCID

Affiliation:

1. Faculty of Applied Mathematics and Informatics, Technical University of Sofia, 8 Kl. Ohridski Blvd., 1000 Sofia, Bulgaria

2. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 8, 1113 Sofia, Bulgaria

3. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 25A, 1113 Sofia, Bulgaria

4. Department of Applied Mathematics and Statistics, University of Ruse, 8 Studentska Str., 7004 Ruse, Bulgaria

Abstract

This paper examines the relationship between the overconvergence of Fourier series and the existence of Hadamard–Ostrowski gaps. Ostrowski’s result on the overconvergence of power series serves as a motivating factor for obtaining a natural generalization: the overconvergence of Fourier series. The connection between Hadamard–Ostrowski gaps and the overconvergence of Fourier series is clarified by applying the Hadamard three-circle theorem and the theory of orthogonal polynomials. Our main result is obtained by applying the Hadamard three-circle theorem.

Publisher

MDPI AG

Link

https://www.mdpi.com/2227-7390/12/7/979/pdf

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