Lectures on Fourier Integrals

Front Cover
Princeton University Press, Sep 21, 1959 - Mathematics - 333 pages

Salomon Bochner’s classic lectures on Fourier integrals from the acclaimed Annals of Mathematics Studies series

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Contents

1 2 3 4 5 CHAPTER
1
Trigonometric Integrals Over Infinite Intervals
5
Order of Magnitude of Trigonometric Integrals
10
Uniform Convergence of Trigonometric Integrals
13
The Cauchy Principal Value of Integrals
18
REPRESENTATION
23
The Dirichlet Integral and Related Integrals
27
8 The Fourier Integral Formula
31
21 Spectral Decomposition of PositiveDefinite Functions An Application to Almost Periodic Functions
97
CHAPTER
104
Differentiation and Integration 25 The DifferenceDifferential Equation 26 The Integral Equation
130
27 Systems of Equations
137
CHAPTER
138
29 Further Particulars About the Functions of
145
30 Further Particulars About the Functions of
153
31 Convergence Theorems
163

9 The Wiener Formula Page 1
35
5
36
10
37
13
38
THE FOURIER INTEGRAL THEOREM 11 The Fourier Integral Theorem and the Inversion Formulas
46
Trigonometric Integrals with e X 12
53
The Absolutely Integrable Functions and Their Summation Their Faltung
54
15 Trigonometric Integrals with
69
17 Evaluation of Certain Repeated Integrals
74
CHAPTER
78
19
83
Sequences of Functions of 2
85
PositiveDefinite Functions
92
32 Multipliers
166
33 Operator Equations
173
34 Functional Equations
178
36 Union of Laplace Integrals
189
37 38 Representation of Given Functions by Laplace Integrals
194
Continuation Harmonic Functions 145
202
CHAPTER
231
REMARKS
281
160
287
MONOTONIC FUNCTIONS STIELTJES INTEGRALS AND HARMONIC ANALYSIS
292
202
332
Copyright

Other editions - View all

Lectures on Fourier Integrals
Salomon Bochner,Salomon Trust
Limited preview - 1959
Lectures on Fourier Integrals. (AM-42), Volume 42
Salomon Bochner Trust
Limited preview - 2016

Common terms and phrases

absolutely convergent absolutely integrable absolutely integrable function arbitrary assertion assumption ax dx belongs bounded function bounded interval Burkhardt Carath Cauchy principal value characteristic function consider constant continuity interval continuous function continuously differentiable convergent to zero converges uniformly defined denote derivative different from zero distribution function equation equivalent essentially convergent essentially equal exists f₁ f₂ Faltung finite interval finite number fixed fn(x following theorem formula 13 Fourier integral func function f(x G. H. Hardy given function Hence holds interval functions inverse formula k-transform Lebesgue Let f(x limit function London Mathematical Society measurable monotonic function monotonically decreasing non-negative obtain Plancherel point set polynomial positive-definite PROOF r-times differentiable relation satisfies solution Stieltjes integral summable tegrable tion transform Trigonometric Integrals valid vanishes variables whole space Wiener

References to this book

Bibliographic information

TitleLectures on Fourier Integrals
Volume 42 of Annals of Mathematics Studies, ISSN 0066-2313
AuthorsSalomon Bochner, Salomon Trust
Translated byMorris Tenenbaum, Harry Pollard
PublisherPrinceton University Press, 1959
ISBN0691079943, 9780691079943
Length333 pages
Subjects › 

Mathematics / Mathematical Analysis
  
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