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

Miroslav Stoenchev, Venelin Todorov () and Slavi Georgiev
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Miroslav Stoenchev: Faculty of Applied Mathematics and Informatics, Technical University of Sofia, 8 Kl. Ohridski Blvd., 1000 Sofia, Bulgaria
Venelin Todorov: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 8, 1113 Sofia, Bulgaria
Slavi Georgiev: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str. Bl. 8, 1113 Sofia, Bulgaria

Mathematics, 2024, vol. 12, issue 7, 1-16

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.

Keywords: Fourier series; overconvergence; orthogonal polynomials; Hadamard–Ostrowski gaps (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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