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

Author

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

  • Slavi Georgiev

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

Suggested Citation

  • Miroslav Stoenchev & Venelin Todorov & Slavi Georgiev, 2024. "Notes on the Overconvergence of Fourier Series and Hadamard–Ostrowski Gaps," Mathematics, MDPI, vol. 12(7), pages 1-16, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:7:p:979-:d:1363588
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