A Panorama of Harmonic Analysis

ISBN-13: 9780883850312 / Angielski / Twarda / 1999 / 370 str.

Steven G. Krantz

Opis

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.