Lectures on Fourier IntegralsThe description for this book, Lectures on Fourier Integrals. (AM-42), Volume 42, will be forthcoming. |
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Contents
BASIC PROPERTIES OF TRIGONOMETRIC INTEGRALS | 1 |
REPRESENTATION AND SUM FORMULAS | 23 |
THE FOURIER INTEGRAL THEOREM | 46 |
13 The Absolutely Integrable Functions Their Faltung | 54 |
STIELTJES INTEGRALS | 78 |
OPERATIONS WITH FUNCTIONS OF THE CLASS | 104 |
GENERALIZED TRIGONOMETRIC INTEGRALS | 138 |
ANALYTIC AND HARMONIC FUNCTIONS | 182 |
FUNCTIONS OF SEVERAL VARIABLES | 231 |
APPENDIX 2614 | 257 |
REMARKS QUOTATIONS | 281 |
MONOTONIC FUNCTIONS STIELTJES INTEGRALS AND HARMONIC ANALYSIS | 292 |
STIELTJES INTEGRALS | 307 |
HARMONIC ANALYSIS | 316 |
| 332 | |
QUADRATIC INTEGRABILITY | 214 |
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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 condition consider constant contained convergent corresponding decreasing defined definition denote derivative determined differentiable e(xa easily equal equation equivalent essentially everywhere example exists expression fact finite interval fixed fn(x follows formula Fourier integral func function f(x further hand Hence holds interval functions inverse k-transform known Let f(x 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 sufficient summable term Theorem theory tion transform uniformly valid vanishes variables write zero
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Bibliographic information
| Title | Lectures on Fourier Integrals Volume 42 of Annals of Mathematics Studies |
| Authors | Salomon Bochner, Salomon Trust |
| Translated by | Morris Tenenbaum, Harry Pollard |
| Publisher | Princeton University Press, 1959 |
| ISBN | 0691079943, 9780691079943 |
| Length | 333 pages |
| Subjects | › Mathematics / Mathematical Analysis |
| Export Citation | BiBTeX EndNote RefMan |