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Distributions : theory and applications

J. J. Duistermaat, Johan A. C. Kolk
Print Book, English, 2010
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Springer, New York, 2010
Cornerstones (Birkhäuser Verlag)
xvi, 445 pages ; 24 cm.
9780817646721, 0817646728
698905709
Analyse fonctionnelle
Espaces de Sobolev
Functional analysis
Sobolev spaces
Theory of distributions (Functional analysis)
Théorie des distributions (Analyse fonctionnelle)
Prefaceix
Standard Notationxv
1 Motivation
1(16)
Problems
13(4)
2 Test Functions
17(16)
Problems
31(2)
3 Distributions
33(12)
Problems
44(1)
4 Differentiation of Distributions
45(6)
Problems
48(3)
5 Convergence of Distributions
51(8)
Problems
54(5)
6 Taylor Expansion in Several Variables
59(6)
Problems
63(2)
7 Localization
65(6)
Problems
69(2)
8 Distributions with Compact Support
71(12)
Problems
81(2)
9 Multiplication by Functions
83(8)
Problems
88(3)
10 Transposition: Pullback and Pushforward
91(24)
Problems
106(9)
11 Convolution of Distributions
115(22)
Problems
132(5)
12 Fundamental Solutions
137(16)
Problems
146(7)
13 Fractional Integration and Differentiation
153(24)
13.1 The Case of Dimension One
153(4)
13.2 Wave Family
157(7)
13.3 Appendix: Euler's Gamma Function
164(4)
Problems
168(9)
14 Fourier Transform
177(44)
Problems
199(22)
15 Distribution Kernels
221(16)
Problems
232(5)
16 Fourier Series
237(34)
Problems
260(11)
17 Fundamental Solutions and Fourier Transform
271(16)
17.1 Appendix: Fundamental Solution of(I - Δ)k
279(3)
Problems
282(5)
18 Supports and Fourier Transform
287(24)
Problems
306(5)
19 Sobolev Spaces
311(10)
Problems
317(4)
20 Appendix: Integration
321(28)
21 Solutions to Selected Problems
349(84)
References433(2)
Index of Notation435(2)
Index437
Bibliographic references (p433-434) and index