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On Fourier Series on the Torus and Fourier Transforms
Mathematical Notes, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Representation of the Fourier Transform by Fourier Series
Journal of Mathematical Imaging and Vision, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Summability of Fourier Series
The Mathematical Gazette, 1931One of the oldest problems in the theory of Fourier series is that of looking for a criterion that a Fourier series shall converge. No one, however, has been able to find a simple, necessary and sufficient condition for this. Thus, for instance, bounded variation of the function is sufficient but not necessary.
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Mathematical Notes, 2020
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Russian Mathematical Surveys, 1961
CONTENTS § 1. Introduction § 2. Definitions and auxiliary propositions § 3. Theorems on summable series § 4. Zahorski' s construction § 5. Haar series § 6. Basic series § 7. Trigonometric series § 8. Walsh series § 9. Series in terms of complete orthonormal systems § 10. Weakly unconditionally convergent series § 11.
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CONTENTS § 1. Introduction § 2. Definitions and auxiliary propositions § 3. Theorems on summable series § 4. Zahorski' s construction § 5. Haar series § 6. Basic series § 7. Trigonometric series § 8. Walsh series § 9. Series in terms of complete orthonormal systems § 10. Weakly unconditionally convergent series § 11.
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Periodica Mathematica Hungarica, 1992
The present work of the author is a sequel to his earlier paper (*) [Acta Math. Hung. 57, No. 1/2, 169-179 (1991; Zbl 0757.41027)]. Several results relating the Hermite-Fourier series are investigated including the norm estimates for the ordinary and conjugate Abel-Poisson means.
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The present work of the author is a sequel to his earlier paper (*) [Acta Math. Hung. 57, No. 1/2, 169-179 (1991; Zbl 0757.41027)]. Several results relating the Hermite-Fourier series are investigated including the norm estimates for the ordinary and conjugate Abel-Poisson means.
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On divergence of Fourier series
The science reports of the Kanazawa University＝金沢大学理科報告, 1970Not ...
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Periodic Hyperfunctions and Fourier Series Fourier Series
1992We have now almost finished the general discussion of hyperfunctions. From now on we shall attempt to apply this general theory to various cases. In this chapter we study periodic hyperfunctions. Then we shall see that the theory of Fourier series is naturally absorbed into the theory of Fourier transformations.
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Canadian Mathematical Bulletin, 1983
AbstractThis note contains a strengthened version of the following well-known theorem: there exists a continuous function whose Fourier series diverges at a point.
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AbstractThis note contains a strengthened version of the following well-known theorem: there exists a continuous function whose Fourier series diverges at a point.
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ON TRIGONOMETRIC FOURIER SERIES
Mathematics of the USSR-Sbornik, 1976This paper studies the problem of the convergence and summability of simple and multiple trigonometric Fourier series.Bibliography: 21 titles.
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