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Introduction to Fourier Analysis on Euclidean Spaces
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Elias M. Stein
Language:
English
Published/Copyright:
1972
About this book
The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.
Topics
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Frontmatter
i -
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Preface
vii -
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Contents
ix -
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I. The Fourier Transform
1 -
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II. Boundary Values of Harmonic Functions
37 -
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III. The Theory of Hp Spaces on Tubes
89 -
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IV. Symmetry Properties o f the Fourier Transform
133 -
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V. Interpolation of Operators
177 -
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VI. Singular Integrals and Systems of Conjugate Harmonic Functions
217 -
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VII. Multiple Fourier Series
245 -
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Bibliography
287 -
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Index
295
Publishing information
Pages and Images/Illustrations in book
eBook published on:
June 2, 2016
eBook ISBN:
9781400883899
Pages and Images/Illustrations in book
Main content:
312
eBook ISBN:
9781400883899
Keywords for this book
Theorem; Fourier transform; Harmonic function; Fourier analysis; Fourier series; Hilbert transform; Cauchy–Riemann equations; Fourier inversion theorem; Fubini's theorem; Norm (mathematics); Poisson summation formula; Bessel function; Existential quantification; Marcinkiewicz interpolation theorem; Distribution (mathematics); Continuous function (set theory); Characterization (mathematics); Linear map; Hardy–Littlewood maximal function; Bounded set (topological vector space); Banach algebra; Paley–Wiener theorem; Trigonometric polynomial; Analytic function; Harmonic analysis; Multiplication operator; Function (mathematics); Partial differential equation; Boundary value problem; Variable (mathematics); Locally integrable function; Plancherel theorem; Mean value theorem; Interpolation theorem; Liouville's theorem (Hamiltonian); Characteristic function (probability theory); Dirichlet problem; Riesz transform; Banach space; Lp space; Radon–Nikodym theorem; Polynomial; Measure (mathematics); Differentiation of integrals; Linear space (geometry); Green's theorem; Representation theorem; Analytic continuation; Support (mathematics); Subharmonic function; Trigonometric series; Holomorphic function; Bounded operator; Interval (mathematics); Quadratic form; Lipschitz continuity; Linear interpolation; Lebesgue measure; Poisson kernel; Radial function; Euclidean space; Principal value; Disk (mathematics); Unit sphere; Hermitian matrix; Borel measure; Hardy's inequality; Series expansion; Function space; Equation
Audience(s) for this book
College/higher education;Professional and scholarly;
