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9781470471996 Academic Inspection Copy

Introduction to Harmonic Analysis

  • ISBN-13: 9781470471996
  • Publisher: AMERICAN MATHEMATICAL SOCIETY
    Imprint: AMERICAN MATHEMATICAL SOCIETY
  • By Ricardo A. Saenz
  • Price: AUD $152.00
  • Stock: 0 in stock
  • Availability: This book is temporarily out of stock, order will be despatched as soon as fresh stock is received.
  • Local release date: 29/11/2023
  • Format: Paperback (216.00mm X 140.00mm) 279 pages Weight: 174g
  • Categories: Calculus & mathematical analysis [PBK]
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This book gives 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. The book motivates the study of harmonic functions by describing the Dirichlet problem, and discussing examples such as solutions to the heat equation in equilibrium, the real and imaginary parts of holomorphic functions, and the minimizing functions of energy. It then leads students through an in-depth study of the boundary behavior of harmonic functions and finishes by developing the theory of harmonic functions defined on fractals domains. The book is designed as a textbook for an introductory course on classical harmonic analysis, or for a course on analysis on fractals. Each chapter contains exercises, and bibliographic and historical notes. The book can also be used as a supplemental text or for self-study.
Ricardo A. Saenz, Universidad de Colima, Mexico.
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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