Harmonic Analysis: A Gentle Introduction

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Jones & Bartlett Learning, 2007 - Mathematics - 219 pages
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Many branches of mathematics come together in harmonic analysis, each adding richness to the subject and each giving insights into this fascinating field. Devito's Harmonic Analysis presents a comprehensive introduction to Fourier analysis and Harmonic analysis and provides numerous examples and models so that students leave with a clear understanding of the theory.
 

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Well I was interested in learning more about the theory behind harmonic analysis and thought this might be a good book. Its new it must be up to date. Up to date for sure but good no. Being a ... Read full review

Contents

Preliminaries
1
Relations and Functions
4
The Real Number System
7
The Complex Number System
11
Analysis
15
Classical Harmonic Analysis
23
The Dirichlet Problem for a Disk
24
Continuous Functions on the Unit Circle
25
Infinite Orthonormal Sets Hilbert Space
96
The Completion
103
Wavelets
107
The Fourier Transform
113
Invertible Elements in f1 Z
119
The Fourier Transform on R
123
Naive Group Theory
128
Not So Naive Group Theory
131

The Method of Fourier
29
Uniform Convergence
32
The Formulas of Euler
39
Cesaro Convergence
43
Fejers Theorem
47
At Last the Solution
52
Extensions of the Classical Theory
57
Functions on Other Intervals
61
Functions with Special Properties
65
Pointwise Convergence of the Fourier Series
70
Fourier Series in Hilbert Space
79
Normed Vector Spaces
80
Convergence in Normed Spaces
84
Inner Product Spaces
90
Finite Fourier Transform
135
An Application
143
Some Algebraic Matters
150
Prime Numbers
154
Eulers Phi Function
159
Abstract Algebra
165
Morphisms
169
Rings
172
Fields
175
Appendix A Linear Algebra
179
Appendix B The Completion
181
Solutions to the Starred Problems
187
Index
213
Copyright

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