Lectures on Fourier IntegralsSalomon Bochner’s classic lectures on Fourier integrals from the acclaimed Annals of Mathematics Studies series |
Contents
BASIC PROPERTIES OF TRIGONOMETRIC INTEGRALS | 1 |
CHAPTER | 23 |
8 The Fourier Integral Formula | 31 |
10 The Poisson Summation Formula | 39 |
27 | 46 |
CHAPTER | 104 |
CHAPTER | 138 |
36 Union of Laplace Integrals | 189 |
APPENDIX | 238 |
Measurability | 264 |
Differentiability | 270 |
Complex Valued Functions | 276 |
MONOTONIC FUNCTIONS STIELTJES INTEGRALS AND HARMONIC ANALYSIS | 292 |
STIELTJES INTEGRALS | 307 |
HARMONIC ANALYSIS | 316 |
| 332 | |
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Common terms and phrases
absolutely convergent absolutely integrable arbitrary assertion assumption ax dx belongs bounded variation Burkhardt Cauchy principal value characteristic function consider constant continuity interval continuous function converges to zero converges uniformly defined denote derivative different from zero distribution function dV(a e(xa equation equivalent essentially convergent essentially equal example exists f f(x Faltung finite interval finite number fixed following theorem Fourier integral func function f(x G. H. Hardy given function Hence holds interval functions inverse formula k-convergent k-transform Laplace integral Let f(x lim f(x limit function Mathematische monotonic functions monotonically decreasing multiplier non-negative obtain point set polynomial positive-definite PROOF prove r-times differentiable relation satisfies sequence solution Stieltjes integral summable tegrable tion transform Trigonometric Integrals uniformly convergent valid vanishes variables Vn(a Wiener x₁ αβ ακ αξ μν φία


