A Panorama of Harmonic Analysis
Cambridge University Press, 1999 M09 2 - 357 páginas
A Panorama of Harmonic Analysis treats the subject of harmonic analysis, from its earliest beginnings to the latest research. Following both an historical and a conceptual genesis, the book discusses Fourier series of one and several variables, the Fourier transform, spherical harmonics, fractional integrals, and singular integrals on Euclidean space. The climax of the book is a consideration of the earlier ideas from the point of view of spaces of homogeneous type. The book culminates with a discussion of wavelets-one of the newest ideas in the subject.
A Panorama of Harmonic Analysis is intended for graduate students, advanced undergraduates, mathematicians, and anyone wanting to get a quick overview of the subject of cummutative harmonic analysis. Applications are to mathematical physics, engineering and other parts of hard science. Required background is calculus, set theory, integration theory, and the theory of sequences and series.
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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