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Keywords = Hadamard–Ostrowski gaps

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16 pages, 310 KiB  
Article
Notes on the Overconvergence of Fourier Series and Hadamard–Ostrowski Gaps
by Miroslav Stoenchev, Venelin Todorov and Slavi Georgiev
Mathematics 2024, 12(7), 979; https://doi.org/10.3390/math12070979 - 25 Mar 2024
Cited by 1 | Viewed by 1231
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 [...] Read more.
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. Full article
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