Book contents
- Frontmatter
- Dedication
- Epigraph
- Contents
- Introduction
- 1 Semigroups and Generators
- 2 The Generation of Semigroups
- 3 Convolution Semigroups of Measures
- 4 Self-Adjoint Semigroups and Unitary Groups
- 5 Compact and Trace Class Semigroups
- 6 Perturbation Theory
- 7 Markov and Feller Semigroups
- 8 Semigroups and Dynamics
- 9 Varopoulos Semigroups
- Notes and Further Reading
- Appendix A The Space C0(Rd)
- Appendix B The Fourier Transform
- Appendix C Sobolev Spaces
- Appendix D Probability Measures and Kolmogorov’s Theorem on Construction of Stochastic Processes
- Appendix E Absolute Continuity, Conditional Expectation and Martingales
- Appendix F Stochastic Integration and Itô’s Formula
- Appendix G Measures on Locally Compact Spaces – Some Brief Remarks
- References
- Index
1 - Semigroups and Generators
Published online by Cambridge University Press: 27 July 2019
Book contents
- Frontmatter
- Dedication
- Epigraph
- Contents
- Introduction
- 1 Semigroups and Generators
- 2 The Generation of Semigroups
- 3 Convolution Semigroups of Measures
- 4 Self-Adjoint Semigroups and Unitary Groups
- 5 Compact and Trace Class Semigroups
- 6 Perturbation Theory
- 7 Markov and Feller Semigroups
- 8 Semigroups and Dynamics
- 9 Varopoulos Semigroups
- Notes and Further Reading
- Appendix A The Space C0(Rd)
- Appendix B The Fourier Transform
- Appendix C Sobolev Spaces
- Appendix D Probability Measures and Kolmogorov’s Theorem on Construction of Stochastic Processes
- Appendix E Absolute Continuity, Conditional Expectation and Martingales
- Appendix F Stochastic Integration and Itô’s Formula
- Appendix G Measures on Locally Compact Spaces – Some Brief Remarks
- References
- Index
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Summary
We define semigroups of linear operators in Banach spaces and introduce their generators (which may be unbounded operators) and their resolvents. A number of examples are given, which will be referred back to throughout the volume.
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- Semigroups of Linear OperatorsWith Applications to Analysis, Probability and Physics, pp. 9 - 30Publisher: Cambridge University PressPrint publication year: 2019
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