Introduction to Fourier analysis on Euclidean spaces


Introduction to Fourier analysis on Euclidean spaces

by Elias M. Stein & Guido Weiss

(Princeton mathematical series, 32)

Princeton University Press, 1990

6th printing

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Bibliography: p. 287-294

Includes index



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.


*Frontmatter, pg. i*Preface, pg. vii*Contents, pg. ix*I. The Fourier Transform, pg. 1*II. Boundary Values of Harmonic Functions, pg. 37*III. The Theory of Hp Spaces on Tubes, pg. 89*IV. Symmetry Properties o f the Fourier Transform, pg. 133*V. Interpolation of Operators, pg. 177*VI. Singular Integrals and Systems of Conjugate Harmonic Functions, pg. 217*VII. Multiple Fourier Series, pg. 245*Bibliography, pg. 287*Index, pg. 295

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