Distributions and Operators
This book gives an introduction to distribution theory, in the spirit of Laurent Schwartz. Additionally, the aim is to show how the theory is combined with the study of operators in Hilbert space by methods of functional analysis, with applications to partial and ordinary differential equations. Her...
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| Format: | Electronic |
| Language: | English |
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New York, NY :
Springer New York,
2009.
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| Series: | Graduate Texts in Mathematics,
252 |
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| Online Access: | https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-387-84895-2 |
Table of Contents:
- Preface
- Motivation and overview
- Function spaces and approximation
- Distributions: Examples and rules of calculus
- Realizations and Sobolev spaces
- Fourier transformation of distributions
- Applications to differential operators: The Sobolev theorem
- Pseudodifferential operators on open sets
- Pseudodifferential operators on manifolds, index of elliptic operators
- Boundary value problems in a constant-coefficient case
- Pseudodifferential boundary operators
- Pseudodifferential methods for boundary value problems
- Unbounded linear operators
- Families of extensions
- Semigroups of operators
- Some notation and prerequisites
- Topological vector spaces
- Function spaces on sets with smooth boundary
- Bibliography
- Index.