Introduction to harmonic analysis

By:

Sáenz, Ricardo A

Series: Student Mathematical Library IAS/ Park City Mathematical Subseries Volume 105Publication details: Providence, Rhode Island: American Mathematical Society, Institute for Advanced Study 2023.Description: xv, 279p.: ill.; pbk.: 22cmISBN:

9781470471996

Subject(s):

DDC classification:

515.2433 SAE

Summary: 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. https://bookstore.ams.org/view?ProductCode=STML/105

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Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar	General	515.2433 SAE (Browse shelf(Opens below))	1	Available		034078

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Previous	515.2433 MEY Wavelets: Calderon-Zygmund and multilinear operators	515.2433 MEY Wavelets and operators	515.2433 RUD Fourier analysis on groups	515.2433 SAE Introduction to harmonic analysis	515.2433 SIL Harmonic analysis on finite groups	515.2433 VAR Introduction to harmonic analysis on semisimple Lie groups	515.2433 VAR Introduction to harmonic analysis on semisimple lie groups	Next

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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.

https://bookstore.ams.org/view?ProductCode=STML/105

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