TY  - BOOK
AU  - Sáenz, Ricardo A.
TI  - Introduction to harmonic analysis
T2  - Student mathematical library, IAS/Park City mathematical subseries
SN  - 9781470471996
U1  - 517.57 
PY  - 2023///
CY  - Rhode Island
PB  - American Mathematical Society
KW  - Harmonic analysis
KW  - Potential theory -- Higher-dimensional theory -- Harmonic, subharmonic, superharmonic functions
KW  - Potential theory -- Higher-dimensional theory -- Integral representations, integral operators, integral equations methods
KW  - Potential theory -- Higher-dimensional theory -- Boundary behavior
KW  - Harmonic analysis on Euclidean spaces -- Harmonic analysis in one variable -- Fourier coefficients, Fourier series of functions with special properties, special Fourier series
KW  - Maximal functions, Littlewood-Paley theory
KW  - Measure and integration -- Classical measure theory -- Fractals
N1  - Includes bibliographical references and index; Undergraduate and graduate students interested in Fourier analysis and harmonic analysis
N2  - 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
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ER  -