Fourier Transforms

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Princeton University Press “[u.a.]”, 1949 - Fourier transformations - 219 pages
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Contents

Preface i
1
2 Riemann Lebesgue Lemma
3
3 Convolution of two functions
5
U Derivatives of a function and its trans form
7
5 Inversion formula
10
6 Uniqueness of Fourier transform
11
7 Summability theorems
13
8 Some applications of summabilitytheorems
19
5 Application of summabilitytheorem
65
6 Norms Continuity Parseval relations
67
8 General summability for radial functions
76
LpSPACES 1 Metric spaces
80
2 Completion of a metric space
81
3 Banach spaces
85
U Linear operations
87
6 Continuity summability and approximation in Ij norm
98

9 Continuity in norm
22
10 Summability in norm
25
11 Derivatives of a function and their trans form
27
12 Degree of approximation
30
13 Abels theorem
35
it Abel and Gauss summability
37
15 Boundary values
41
16 Mean values
47
17 Tauberian theorems
50
Convolution
57
2 Uniqueness theorem
59
3 Gauss summability formula
61
4 Gauss summability theorem
64
FOURIER TRANSFORMS IN
104
1 Transformations in Hilbert space 10k 2 Plancherels theorem
105
3 General summability
113
4 Several variables
117
5 Radial functions
121
6 Derivatives and their transforms
123
7 Boundary values
132
8 Simple type of bounded transformation
138
GENERAL TRANSFORMS IN
150
GENERAL TAUBERIAN THEOREMS
171
NOTES
209
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