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 Trigonometric Integrals Over Finite Intervals | 1 |
2 Trigonometric Integrals Over Infinite Intervals | 5 |
3 Order of Magnitude of Trigonometric Integrals | 10 |
4 Uniform Convergence of Trigonometric Integrals | 13 |
5 The Cauchy Principal Value of Integrals | 18 |
REPRESENTATION AND SUM FORMULAS | 23 |
7 The Dirichlet Integral and Related Integrals | 27 |
8 The Fourier Integral Formula | 31 |
26 The Integral Equation | 130 |
27 Systems of Equations | 134 |
GENERALIZED TRIGONOMETRIC INTEGRALS | 138 |
29 Further Particulars About the functions of FK | 145 |
30 Further Particulars About the functions of Ik | 153 |
31 Convergence Theorems | 160 |
32 Multipliers | 166 |
33 Operator Equations | 173 |
9 The Wiener Formula | 35 |
10 The Poisson Summation Formula | 39 |
THE FOURIER INTEGRAL THEOREM | 46 |
12 Trigonometric Integrals with e | 51 |
13 The Absolutely Integrable Functions Their Faltung and Their Summation | 54 |
14 Trigonometric Integrals with Rational Functions | 63 |
17 Evaluation of Certain Repeated Integrals | 74 |
STIELTJES INTEGRALS | 78 |
19 Sequences of Functions of P | 89 |
20 PositiveDefinite Functions | 92 |
21 Spectral Decomposition of PositiveDefinite Functions An Application to Almost Periodic Functions | 97 |
OPERATIONS WITH FUNCTIONS OF THE CLASS 7 | 104 |
23 Multipliers | 108 |
24 Differentiation and Integration | 114 |
25 The DifferenceDifferential Equation | 120 |
34 Functional Equations | 178 |
ANALYTIC AND HARMONIC FUNCTIONS | 182 |
36 Union of Laplace Integrals | 189 |
37 Representation of Given Functions by Laplace Integrals | 194 |
38 Continuation Harmonic Functions | 202 |
QUADRATIC INTEGRABILITY | 214 |
FUNCTIONS OF SEVERAL VARIABLES | 231 |
APPENDIX 2644 | 257 |
REMARKS QUOTATIONS | 281 |
MONOTONIC FUNCTIONS STIELTJES INTEGRALS AND HARMONIC ANALYSIS | 292 |
STIELTJES INTEGRALS | 307 |
HARMONIC ANALYSIS | 316 |
| 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 condition consider constant contained convergent decreasing defined definition denote derivative determined differentiable distribution 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 limit manner mean measurable monotonically multiplier necessary obtain partial particular point set polynomial positive PROOF prove r-times differentiable relation 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, ISSN 0066-2313 |
| 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 |