TABLE OF CONTENTS
Abstract vi
Acknowledgments vii
Introduction and Results 1
Chapter I. Theory of Feller Semigroups 11
1.1 Markov Transition Functions and Feller Semigroups 11
1.2 Generation Theorems of Feller Semigroups 14
Chapter II. Theory of Pseudo-Differential Operators 16
2.1 Function Spaces 16
2.2 Pseudo-Differential Operators 19
2.3 Unique Solvability Theorem for Pseudo-Differential
Operators 23
Chapter III. Proof of Theorem 1 30
3.1 General Existence Theorem for Feller Semigroups 31
3.2 Proof of Theorem 1 38
Chapter IV. Proof of Theorem 2 47
4.1 The Space C0(D\M) 48
4.2 Proof of Theorem 2 49
Appendix The Maximum Principle 62
References 64
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