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      Fourier Series in Several Variables with Applications to Partial Differential Equations
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      Book

      Fourier Series in Several Variables with Applications to Partial Differential Equations

      DOI link for Fourier Series in Several Variables with Applications to Partial Differential Equations

      Fourier Series in Several Variables with Applications to Partial Differential Equations book

      Fourier Series in Several Variables with Applications to Partial Differential Equations

      DOI link for Fourier Series in Several Variables with Applications to Partial Differential Equations

      Fourier Series in Several Variables with Applications to Partial Differential Equations book

      ByVictor L. Shapiro
      Edition 1st Edition
      First Published 2011
      eBook Published 10 May 2011
      Pub. Location New York
      Imprint Chapman and Hall/CRC
      DOI https://doi.org/10.1201/b10811
      Pages 352
      eBook ISBN 9780429107559
      Subjects Mathematics & Statistics
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      Shapiro, V.L. (2011). Fourier Series in Several Variables with Applications to Partial Differential Equations (1st ed.). Chapman and Hall/CRC. https://doi.org/10.1201/b10811

      ABSTRACT

      Discussing many results and studies from the literature, this work illustrates the value of Fourier series methods in solving difficult nonlinear PDEs. Using these methods, the author presents results for stationary Navier-Stokes equations, nonlinear reaction-diffusion systems, and quasilinear elliptic PDEs and resonance theory. He also establishes the connection between multiple Fourier series and number theory, presents the periodic Ca-theory of Calderon and Zygmund, and explores the extension of Fatou's famous work on antiderivatives and nontangential limits to higher dimensions. The importance of surface spherical harmonic functions is emphasized throughout.

      TABLE OF CONTENTS

      chapter Chapter 1|38 pages

      Summability of Multiple Fourier Series

      chapter Chapter 2|40 pages

      Conjugate Multiple Fourier Series

      chapter Chapter 3|59 pages

      Uniqueness of Multiple Trigonometric Series

      chapter Chapter 4|19 pages

      Positive Definite Functions

      chapter Chapter 5|60 pages

      Nonlinear Partial Differential Equations

      chapter Chapter 6|57 pages

      The Stationary Navier-Stokes Equations

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