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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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Mathematical Notes, 2020
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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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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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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
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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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 Transform
1998In this chapter we look at some of the eigenfunction expansions in terms of Fourier series. We develop the Fourier transform and use it to solve the heat equation again. We also give a brief treatment of the discrete Fourier transform (DFT) and the fast Fourier transform (FFT).
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