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.
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Appendix argument atom ball Banach space boundary bounded on Lp calculate Calderon-Zygmund Chapter characteristic function circle group classical compact constant continuous functions define definition denote dense differential Dirichlet equation estimate Euclidean space fact Figure finite follows formula Fourier analysis Fourier coefficient Fourier multiplier Fourier series Fourier transform fractional integral func Functional Analysis Haar series Hardy spaces Hardy-Littlewood maximal harmonic analysis Hilbert space Hilbert transform holomorphic homogeneous of degree homogeneous type inequality inner product integral operators interval Lebesgue Lemma linear operator Lp norm Lp(RN mapping mathematical maximal function measurable function operator norm orthogonal orthonormal basis partial summation partial sums pointwise Poisson kernel polygonal Proof properties Proposition prove reader result Riesz rotation satisfies sequence singular integral space of homogeneous spherical harmonics sprouting summability kernels tion topology triangle trigonometric polynomial uniformly variable vector wavelet weak-type zero