Lectures on Fourier Integrals. (AM-42), Volume 42Salomon Bochner’s classic lectures on Fourier integrals from the acclaimed Annals of Mathematics Studies series |
Contents
| 1 | |
REPRESENTATION AND SUM FORMULAS | 23 |
THE FOURIER INTEGRAL THEOREM | 46 |
STIELTJES INTEGRALS | 78 |
OPERATIONS WITH FUNCTIONS OF THE CLASS JO | 104 |
GENERALIZED TRIGONOMETRIC INTEGRALS | 138 |
ANALYTIC AND HARMONIC FUNCTIONS | 182 |
QUADRATIC INTEGRABILITY | 214 |
FUNCTIONS OF SEVERAL VARIABLES | 231 |
APPENDIX | 264 |
REMARKS QUOTATIONS | 281 |
MONOTONIC FUNCTIONS STIELTJES INTEGRALS AND HARMONIC ANALYSIS | 293 |
| 332 | |
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Common terms and phrases
absolutely integrable addition agrees analytic apply arbitrarily arbitrary assertion assume assumption ax dx belongs bounded Burkhardt Cauchy principal value complex con condition consider constant contained continuously differentiable convergent corresponding cp(a decreasing defined definition denote derivative determined differentiable easily equal equation equivalent essentially everywhere example exists expression fact finite interval fixed fn(x follows formula Fourier integral func function f(x further given hand Hence holds interval function inverse k-transform limit manner mean measurable monotonically multiplier necessary obtain partial particular point set polynomial positive PROOF prove r-times differentiable relation REMARK replaced representation respect satisfies sequence side solution space sufficient summable term Theorem theory tion transform uniformly valid vanishes variables write zero