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Fourier analysis.

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Harmonic analysis. Fourier analysis --- Fourier analysis.

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This unique book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.

Fourier analysis. --- Harmonic analysis. Fourier analysis

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The purpose of this paper is to make a study of special classes of trigonometric series in k-dimensions. These series are analogues of one-dimensional series which have shed light on problems in Fourier analysis in one dimension. This study is carried out in parts I-III. In part IV, we give applications to various problems in analysis, and applications and their relations to known theorems are discussed in detail.

Fourier series. --- Fourier analysis. --- Fourier analysis. --- Fourier series.

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Fourier analysis --- Problems, exercises, etc --- Problems, exercises, etc. --- Harmonic analysis. Fourier analysis --- Fourier, Analyse de --- Fourier analysis - Problems, exercises, etc.