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This volume will be of great appeal to both advanced students and researchers. For the former, it serves as an effective introduction to three interrelated subjects of analysis: semigroups, Markov processes and elliptic boundary value problems. For the latter, it provides a new method for the analysis of Markov processes, a powerful method clearly capable of extensive further development.
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From the reviews:
"This book is devoted to the study of certain uniformly elliptic boundary value problems and associated semigroups. ... The main results are all laid out in the introduction, so it is always clear where the book is headed. ... For the probabilist, the book provides a good introduction to modern sophisticated results on analytical problems associated with diffusion processes with possibly additional Lèvy-type jumps. In some cases, the book may also be a useful reference ... ." (Jan M. Swart, Jahresberichte der Deutschen Mathematiker Vereinigung, November, 2005)
"This book by Kazuaki Taira contains a detailed study of semigroups, elliptical boundary value problems, Markov processes and the relations between these mathematical concepts. ... The book grew out of a series of lectures and lecture notes; this facilitates its use for teaching at the graduate level. The presentation is detailed and clear ... . I would recommend the book for graduate students or researchers interested mainly in the analytical aspects of Markov process theory ... ." (R. Frey, ZAA - Zeitschrift für Analysis und ihre Anwendungen, Vol. 23 (3), 2004)
"In this book the author proposes the study of three interrelated subjects in analysis: semigroups, elliptic boundary value problems and Markov processes. ... The well chosen material given in an appropriate form and style makes the book very useful for the university students as well as for mathematicians with interests in probability theory, functional analysis and partial differential equations." (Mikhail P. Moklyachuk, Zentralblatt MATH, Vol. 1035, 2004)
"The book is devoted to the generation of analytic Feller semigroups by operators corresponding to boundary value problems for second order elliptic differential and integro-differential equations. ... the present book is a valuable contribution to a rich field of mathematics emerging at the interface of functional analysis,partial differential equations, and stochastic processes." (Anatoly N. Kochubei, Mathematical Reviews, 2004 i)
"This book is devoted to the study of certain uniformly elliptic boundary value problems and associated semigroups. ... The main results are all laid out in the introduction, so it is always clear where the book is headed. ... For the probabilist, the book provides a good introduction to modern sophisticated results on analytical problems associated with diffusion processes with possibly additional Lèvy-type jumps. In some cases, the book may also be a useful reference ... ." (Jan M. Swart, Jahresberichte der Deutschen Mathematiker Vereinigung, November, 2005)
"This book by Kazuaki Taira contains a detailed study of semigroups, elliptical boundary value problems, Markov processes and the relations between these mathematical concepts. ... The book grew out of a series of lectures and lecture notes; this facilitates its use for teaching at the graduate level. The presentation is detailed and clear ... . I would recommend the book for graduate students or researchers interested mainly in the analytical aspects of Markov process theory ... ." (R. Frey, ZAA - Zeitschrift für Analysis und ihre Anwendungen, Vol. 23 (3), 2004)
"In this book the author proposes the study of three interrelated subjects in analysis: semigroups, elliptic boundary value problems and Markov processes. ... The well chosen material given in an appropriate form and style makes the book very useful for the university students as well as for mathematicians with interests in probability theory, functional analysis and partial differential equations." (Mikhail P. Moklyachuk, Zentralblatt MATH, Vol. 1035, 2004)
"The book is devoted to the generation of analytic Feller semigroups by operators corresponding to boundary value problems for second order elliptic differential and integro-differential equations. ... the present book is a valuable contribution to a rich field of mathematics emerging at the interface of functional analysis,partial differential equations, and stochastic processes." (Anatoly N. Kochubei, Mathematical Reviews, 2004 i)