Professor Kazuaki TAIRA, born in Tokyo, Japan in 1946, served for many years as a Professor of Mathematics at the University of Tsukuba (1998-2009). He received his Bachelor of Science in 1969 from the University of Tokyo, Japan and his Master of Science in 1972 from Tokyo Institute of Technology, Japan, where he served as an assistant from 1972 to 1978. The Doctor of Science degree was awarded to him in 1976 by the University of Tokyo and in 1978 the Doctorat d'Etat degree was given to him by Universite de Paris-Sud, France. He held a French government scholarship from 1976 to 1978.He has also served as a member of the Institute for Advanced Study, USA (1980-1981), as an Associate Professor at the University of Tsukuba (1981-1995) and as a Professor at Hiroshima University, Japan (1995-1998). In 1998, he accepted an invitation from the University of Tsukuba to teach there again as a Professor. Since 2009, he has also been a part-time Professor at Waseda University. His current research interests are in the study of three interrelated subjects in analysis: semi groups, elliptic boundary value problems and Markov processes.

• 1.Introduction and Main Results.- Part I Elements of Analysis.- 2.Elements of Probability Theory.- 3.Elements of Functional Analysis.- 4.Theory of Semigroups.- Part II Elements of Partial Differential Equations.- 5.Theory of Distributions.- 6.Sobolev and Besov Spaces.- 7.Theory of Pseudo-Differential Operators.- 8.Waldenfels Operators and Maximum Principles.- Part III Markov Processes, Semigroups and Boundary Value problems.- 9.Markov Processes, Transition Functions and Feller Semigroups.- 10.Feller Semigroups and Elliptic Boundary Value Problems.- 11.Proof of Theorem 1.3.- 12.Markov Processes Revisited.- 13.Concluding Remarks.- Appendix: Boundedness of Pseudo-Differential Operators.- References.- Index.

Professor Kazuaki TAIRA, born in Tokyo, Japan in 1946, served for many years as a Professor of Mathematics at the University of Tsukuba (1998-2009). He received his Bachelor of Science in 1969 from the University of Tokyo, Japan and his Master of Science in 1972 from Tokyo Institute of Technology, Japan, where he served as an assistant from 1972 to 1978. The Doctor of Science degree was awarded to him in 1976 by the University of Tokyo and in 1978 the Doctorat d'Etat degree was given to him by Universite de Paris-Sud, France. He held a French government scholarship from 1976 to 1978.He has also served as a member of the Institute for Advanced Study, USA (1980-1981), as an Associate Professor at the University of Tsukuba (1981-1995) and as a Professor at Hiroshima University, Japan (1995-1998). In 1998, he accepted an invitation from the University of Tsukuba to teach there again as a Professor. Since 2009, he has also been a part-time Professor at Waseda University. His current research interests are in the study of three interrelated subjects in analysis: semi groups, elliptic boundary value problems and Markov processes.

• 1.Introduction and Main Results.- Part I Elements of Analysis.- 2.Elements of Probability Theory.- 3.Elements of Functional Analysis.- 4.Theory of Semigroups.- Part II Elements of Partial Differential Equations.- 5.Theory of Distributions.- 6.Sobolev and Besov Spaces.- 7.Theory of Pseudo-Differential Operators.- 8.Waldenfels Operators and Maximum Principles.- Part III Markov Processes, Semigroups and Boundary Value problems.- 9.Markov Processes, Transition Functions and Feller Semigroups.- 10.Feller Semigroups and Elliptic Boundary Value Problems.- 11.Proof of Theorem 1.3.- 12.Markov Processes Revisited.- 13.Concluding Remarks.- Appendix: Boundedness of Pseudo-Differential Operators.- References.- Index.

Professor Kazuaki TAIRA, born in Tokyo, Japan in 1946, served for many years as a Professor of Mathematics at the University of Tsukuba (1998-2009). He received his Bachelor of Science in 1969 from the University of Tokyo, Japan and his Master of Science in 1972 from Tokyo Institute of Technology, Japan, where he served as an assistant from 1972 to 1978. The Doctor of Science degree was awarded to him in 1976 by the University of Tokyo and in 1978 the Doctorat d'Etat degree was given to him by Universite de Paris-Sud, France. He held a French government scholarship from 1976 to 1978.He has also served as a member of the Institute for Advanced Study, USA (1980-1981), as an Associate Professor at the University of Tsukuba (1981-1995) and as a Professor at Hiroshima University, Japan (1995-1998). In 1998, he accepted an invitation from the University of Tsukuba to teach there again as a Professor. Since 2009, he has also been a part-time Professor at Waseda University. His current research interests are in the study of three interrelated subjects in analysis: semi groups, elliptic boundary value problems and Markov processes.

• 1.Introduction and Main Results.- Part I Elements of Analysis.- 2.Elements of Probability Theory.- 3.Elements of Functional Analysis.- 4.Theory of Semigroups.- Part II Elements of Partial Differential Equations.- 5.Theory of Distributions.- 6.Sobolev and Besov Spaces.- 7.Theory of Pseudo-Differential Operators.- 8.Waldenfels Operators and Maximum Principles.- Part III Markov Processes, Semigroups and Boundary Value problems.- 9.Markov Processes, Transition Functions and Feller Semigroups.- 10.Feller Semigroups and Elliptic Boundary Value Problems.- 11.Proof of Theorem 1.3.- 12.Markov Processes Revisited.- 13.Concluding Remarks.- Appendix: Boundedness of Pseudo-Differential Operators.- References.- Index.