Introduction to harmonic analysis
Material type:
TextLanguage: English Series: Student mathematical library, IAS/Park City mathematical subseries ; volume 105.Publication details: Rhode Island : American Mathematical Society, 2023. Description: xv, 279pISBN: 9781470471996Subject(s): Harmonic analysis | Potential theory -- Higher-dimensional theory -- Harmonic, subharmonic, superharmonic functions | Potential theory -- Higher-dimensional theory -- Integral representations, integral operators, integral equations methods | Potential theory -- Higher-dimensional theory -- Boundary behavior | Harmonic analysis on Euclidean spaces -- Harmonic analysis in one variable -- Fourier coefficients, Fourier series of functions with special properties, special Fourier series | Maximal functions, Littlewood-Paley theory | Measure and integration -- Classical measure theory -- FractalsDDC classification: 517.57 Online resources: Table of Contents | Reviews 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.
| Item type | Current library | Call number | Status | Date due | Barcode |
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Book
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SMS Library | 517.57 SAE-I (Browse shelf(Opens below)) | Available | 25209 |
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| 517.57 KRA-D Discrete analogues in harmonic analysis : bourgain, stein, and beyond | 517.57 MIK-P Partial differential equation | 517.57 PER-H Harmonic analysis : from fourier to wavelets | 517.57 SAE-I Introduction to harmonic analysis | 517.57 SIN-T Theory of semigroups and applications | 517.57 TEO-C Computational signal processing with wavelets | 517.57 THA-H Harmonic analysis on the heisenberg group |
Includes bibliographical references and index.
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.
Undergraduate and graduate students interested in Fourier analysis and harmonic analysis.
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