A Panorama of Harmonic AnalysisCambridge University Press, 1999 M09 2 - 357 páginas 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. |
Contenido
Fourier Series Basics | 31 |
The Fourier Transform | 95 |
Multiple Fourier Series | 121 |
Spherical Harmonics | 171 |
Fractional Integrals Singular Integrals | 199 |
Modern Theories of Integral Operators | 235 |
Wavelets | 273 |
A Retrospective | 313 |
Table of Notation | 327 |
| 347 | |
Términos y frases comunes
Appendix atomic ball Banach space bounded on LP calculate Calderón-Zygmund Chapter characteristic function circle group classical compact complex constant continuous functions define definition denote dense differential disjoint equation Euclidean space fact Fefferman Figure finite follows formula Fourier analysis Fourier multiplier Fourier series Fourier transform fractional integral func function f Hardy spaces harmonic analysis Hilbert space Hilbert transform homogeneous of degree homogeneous type inequality inner product integral operators interval L¹ function L¹(RN Lebesgue Lemma Let f linear operator LP norm LP RN mapping Math mathematical maximal function measurable function notation operator norm orthogonal partial summation partial sums pointwise Poisson kernel Proof properties Proposition prove reader result Riesz Section singular integral space of homogeneous spherical harmonics sprouting summability kernels theorem tion topology trigonometric polynomial uniformly variable vector wavelet weak-type zero