Description

Book Synopsis
Provides a self-contained introduction to the modern ideas and problems of harmonic analysis. Intended for third- and fourth-year undergraduates, the book only requires basic knowledge of real analysis, and covers necessary background in measure theory, Lebesgue integration and approximation theorems.

Table of Contents
  • Motivation and preliminaries
  • Basic properties
  • Fourier series
  • Poisson kernel in the half-space
  • Measure theory in Euclidean space
  • Lebesgue integral and Lebesgue spaces
  • Maximal functions
  • Fourier transform
  • Hilbert transform
  • Mathematics of fractals
  • The Laplacian on the Sierpinski gasket
  • Eigenfunctions of the Laplacian
  • Harmonic functions on post-critically finite sets
  • Some results from real analysis
  • Bibliography
  • Index.

Introduction to Harmonic Analysis

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    A Paperback by Ricardo A. Saenz

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      Book details

      Publisher American Mathematical Society
      Published 8/31/2023 12:00:00 AM
      ISBN-13 9781470471996
      978-1470471996
      ISBN-10 147047199X

      Description

      Book Synopsis
      Provides a self-contained introduction to the modern ideas and problems of harmonic analysis. Intended for third- and fourth-year undergraduates, the book only requires basic knowledge of real analysis, and covers necessary background in measure theory, Lebesgue integration and approximation theorems.

      Table of Contents
      • Motivation and preliminaries
      • Basic properties
      • Fourier series
      • Poisson kernel in the half-space
      • Measure theory in Euclidean space
      • Lebesgue integral and Lebesgue spaces
      • Maximal functions
      • Fourier transform
      • Hilbert transform
      • Mathematics of fractals
      • The Laplacian on the Sierpinski gasket
      • Eigenfunctions of the Laplacian
      • Harmonic functions on post-critically finite sets
      • Some results from real analysis
      • Bibliography
      • Index.

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