A Panorama of Harmonic Analysis

Tracing a path from the earliest beginnings of Fourier series through to the latest research A Panorama of Harmonic Analysis discusses Fourier series of one and several variables, the Fourier transform, spherical harmonics, fractional integrals, and singular integrals on Euclidean space. The climax is a consideration of ideas from the point of view of spaces of homogeneous type, which culminates in a discussion of wavelets. This book is intended for graduate students and advanced undergraduates, and mathematicians of whatever background who want a clear and concise overview of the subject of commutative harmonic analysis.

Spis treści:
0. An overview of measure theory and functional analysis
1. Fourier series basics
2. The Fourier transform
3. Multiple Fourier series
4. Spherical harmonics
5. Fractional integrals, singular integrals and Hardy spaces
6. Modern theories of integral operators
7. Wavelets
8. A retrospective
Appendices.