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Harmonic analysis. Fourier analysis --- Ergodic theory. Information theory

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This book presents the basic ideas in Fourier analysis and its applications to the study of partial differential equations. It also covers the Laplace and Zeta transformations and the fundaments of their applications. The author has intended to make his exposition accessible to readers with a limited background, for example, those not acquainted with the Lebesgue integral or with analytic functions of a complex variable. At the same time, he has included discussions of more advanced topics such as the Gibbs phenomenon, distributions, Sturm-Liouville theory, Cesaro summability and multi-dimensional Fourier analysis, topics which one usually will not find in books at this level. Many of the chapters end with a summary of their contents, as well as a short historical note. The text contains a great number of examples, as well as more than 350 exercises. In addition, one of the appendices is a collection of the formulas needed to solve problems in the field. Anders Vretblad is Senior Lecturer of Mathematics at Uppsala University, Sweden.

Fourier analysis --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Analyse de Fourier --- EPUB-LIV-FT SPRINGER-B --- Mathematics. --- Fourier analysis. --- Fourier Analysis. --- Analysis, Fourier --- Mathematical analysis

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Fourier analysis. --- Analyse de Fourier --- Fourier Analysis. --- 519.246 --- 517.518 --- 517.518.4 --- 517.518.5 --- Statistics of stochastic processes. Estimation of stochastic processes. Hypothesis testing. Statistics of point processes. Time series analysis. Auto-correlation. Regression --- Metric theory of functions --- Trigonometric series --- Theory of the Fourier integral --- 517.518.5 Theory of the Fourier integral --- 517.518.4 Trigonometric series --- 517.518 Metric theory of functions --- 519.246 Statistics of stochastic processes. Estimation of stochastic processes. Hypothesis testing. Statistics of point processes. Time series analysis. Auto-correlation. Regression --- Fourier analysis --- Analysis, Fourier --- Mathematical analysis --- Fourier, Analyse de --- Fourier, Séries de

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Functions, Special --- Orthogonal polynomials --- Academic collection --- 517.518.8 --- 517.518.8 Approximation of functions by polynomials and their generalizations --- Approximation of functions by polynomials and their generalizations --- Special functions --- Fourier analysis --- Functions, Orthogonal --- Polynomials --- Mathematical analysis --- Special functions. --- Computer mathematics. --- Topological groups. --- Lie groups. --- Combinatorics. --- Differential equations. --- Fourier analysis. --- Special Functions. --- Computational Science and Engineering. --- Topological Groups, Lie Groups. --- Ordinary Differential Equations. --- Fourier Analysis. --- Analysis, Fourier --- 517.91 Differential equations --- Differential equations --- Combinatorics --- Algebra --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups --- Groups, Topological --- Continuous groups --- Computer mathematics --- Electronic data processing --- Mathematics