Introduction to Fourier Analysis on Euclidean SpacesPrinceton University Press, 1971. 11. 21. - 297페이지 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. |
목차
The Fourier Transform | 1 |
Boundary Values of Harmonic Functions | 37 |
The Theory of Hº Spaces on Tubes | 89 |
Symmetry Properties of the Fourier Transform | 133 |
Interpolation of Operators | 177 |
Singular Integrals and Systems of Conjugate | 217 |
Multiple Fourier Series | 245 |
| 287 | |
| 295 | |
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argument Banach space Borel measure boundary values bounded C₁ Chapter characteristic function cone consider continuous function convergence convolution Corollary denote domain En+1 Ent+1 equality everywhere exists a constant extend f belongs f₁ fact finite Borel measure Fourier series Fourier transform function defined function f harmonic functions Hilbert transform immediate consequence implies inequality interpolation theorem L¹(En L2-norm L²(En Lemma linear operators Lº(En LP(En mapping maximal function Moreover n-tuple nonnegative nontangential limit norm obtain orthogonal p₁ Plancherel theorem Poisson integral Poisson kernel Poisson summation formula polynomials proof of Theorem proved real numbers restricted rotation satisfying singular integral operators spherical harmonics subharmonic subset suffices to show summability Suppose f tempered distribution tends Theorem 1.1 unit sphere variables x₁ y₁ Zygmund ΜΕΛ Ση