Distributions and Convolution Equations

Front Cover
To make their work more accessible to readers new to this field, the authors restrict initial treatment of problems to the half-line and formulate only principal results, in their simplest form. Special results and possible generalizations are presented as problems and exercises. For this reason this work is recommended not only for experts in the field of partial differential equations, but also for senior undergraduate and graduate students less familiar with this area.
The authors apply the results of many years of their own original research to a systematic presentation of the theory of distributions. The first part of their monograph is devoted to the Cauchy problem. The authors show that Petrovskii's classic theory of the correctness of the Cauchy problem for general differential operators with constant convolution equations in certain spaces of distributions. The second part deals with the Wiener-Hopf equation and related topics in the theory of boundary value problems for convolution equa
 

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Contents

1 Spaces of Testfunctions and Distributions
3
2 The Scale of Hilbert Spaces Associated with S Sobolev
18
Appendix to 2
31
3 Convolution in Spaces of Tempered Distributions
37
Appendix to 3
48
5 The Spaces Sto and the Related Scales
60
Appendix to Chapter 1 Scales of Topological Linear Spaces
73
Homogeneous Cauchy Problem for Convolution
93
Exponentially Correct Differential Operators
240
Equations
249
Appendix to 1
274
Cauchy Problem for Differential and Pseudodifferential
311
Appendix to 1
342
3 Pseudodifferential Equations in R the Case of the Spaces
368
4 Exponentially Correct Differential Operators with Variable
378
WienerHopf Convolutors and Boundary Value
383

Appendix to şi
113
3 Scales of Spaces of Functions Defined in R
123
4 Convolution Operators and Convolution Equations in Spaces
145
5 Convolutors and Convolution Equations in Spaces
173
Convolution Equations in Spaces of Exponentially
193
2 The Homogeneous Cauchy Problem in Spaces
218
Appendix to 2
232
2 Factorization of WienerHopf Convolutors
393
Appendix to 2
402
The WienerHopf Equation on a Halfline
410
The WienerHopf Equation in a Halfspace
430
References
453
Subject Index
463
Copyright

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