Lectures on Fourier Integrals

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Princeton University Press, Sep 21, 1959 - Mathematics - 333 pages
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The 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
SYMBOLS INDEX
332
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