Semigroups of linear operators with applications to analysis, probability and physics

Cover......Page 1
LONDON MATHEMATICAL SOCIETY STUDENT TEXTS......Page 3
Semigroups of Linear Operators:With Applications to Analysis, Probability and Physics......Page 5
Copyright......Page 6
Dedication......Page 7
Epigraph......Page 8
Contents......Page 9
Introduction......Page 13
1 Semigroups and Generators......Page 21
2 The Generation of Semigroups......Page 43
3 Convolution Semigroups of Measures......Page 58
4 Self-Adjoint Semigroups and Unitary Groups......Page 95
5 Compact and Trace Class Semigroups......Page 114
6 Perturbation Theory......Page 128
7 Markov and Feller Semigroups......Page 141
8 Semigroups and Dynamics......Page 161
9 Varopoulos Semigroups......Page 178
Notes and Further Reading......Page 191
Appendix A.The Space C0(Rd)......Page 194
Appendix B.The Fourier Transform......Page 198
Appendix C.Sobolev Spaces......Page 202
Appendix D.Probability Measures and Kolmogorov’sTheorem on Construction of StochasticProcesses......Page 206
Appendix E.Absolute Continuity, Conditional Expectationand Martingales......Page 209
Appendix F.Stochastic Integration and Itô’s Formula......Page 217
Appendix G.Measures on Locally Compact Spaces – SomeBrief Remarks......Page 224
References......Page 226
Index......Page 231