On the Absolute Convergence of Fourier Series of Almost Periodic Functions

The paper investigates sufficient conditions for the absolute convergence of trigonometric Fourier series of almost-periodic functions in the sense of Besikovitch in the case when the Fourier exponents have a single limiting point at infinity. A higher-order modulus of continuity is used as a struct...

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Bibliographic Details
Published in:Russian mathematics 2024-04, Vol.68 (4), p.60-71
Main Authors: Khasanov, Yu. Kh, Talbakov, F. M.
Format: Article
Language:English
Subjects:
Continuity (mathematics)
Convergence
Fourier series
Mathematics
Mathematics and Statistics
Periodic functions
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Summary:The paper investigates sufficient conditions for the absolute convergence of trigonometric Fourier series of almost-periodic functions in the sense of Besikovitch in the case when the Fourier exponents have a single limiting point at infinity. A higher-order modulus of continuity is used as a structural characteristic of the function under consideration.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X24700282