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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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Mathematical Notes, 2020
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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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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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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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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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Introduction to Fourier Series
2013We start the book by considering the series \(\mathop {\Sigma }\nolimits _{n=1}^\infty {\mathrm{sin}(n x) \over n},\) a nice example of a Fourier series. This series converges for all real numbers x, but the issue of convergence is delicate. We introduce summation by parts as a tool for handling some conditionally convergent series of this sort.
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Fourier Series and Fourier Transforms
2003In Chapter 3, we touched upon the analogy between the diffraction of x-rays and that of visible light. Here, we extend that discussion and consider some aspects of Fourier series and Fourier transforms.
Mark Ladd, Rex Palmer
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Fourier series and Fourier transforms
2013Some of the most versatile mathematical functions are the trigonometric functions sine and cosine. As a result, it is often very helpful to express a general function as a linear combination of these functions and then to carry out manipulations on the resulting series.
Peter Atkins +2 more
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The Fourier Series and Fourier Transform
2020We encountered the Fourier series in passing in Chap. 5. Then it was just to illustrate the importance of sine waves as a fundamental waveform from which more complex ones such as a square wave could be constructed by adding them with different frequencies and amplitudes.
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