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 eBook |
| 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: | Full Text via HEAL-Link |
Table of Contents:
- Distributions and derivatives
- Motivation and overview
- Function spaces and approximation
- Distributions. Examples and rules of calculus
- Extensions and applications
- Realizations and Sobolev spaces
- Fourier transformation of distributions
- Applications to differential operators. The Sobolev theorem
- Pseudodifferential operators
- Pseudodifferential operators on open sets
- Pseudodifferential operators on manifolds, index of elliptic operators
- Boundary value problems
- Boundary value problems in a constant-coefficient case
- Pseudodifferential boundary operators
- Pseudodifferential methods for boundary value problems
- Topics on Hilbert space operators
- Unbounded linear operators
- Families of extensions
- Semigroups of operators.
