Perturbations of Positive Semigroups with Applications

Basic Facts from Functional Analysis and Banach Lattices.- An Overview of Semigroup Theory.- Some Classical Perturbation Results.- Positive Perturbations of Positive Semigroups.- Substochastic Semigroups and Generator Characterization.- Applications to Birth-and-death Problems.- Applications to Pure Fragmentation Problems.- Fragmentation with Growth and Decay.- Applications to Kinetic Theory.- Singularly Perturbed Inelastic Collision Models.

From the reviews:"Several books of different sorts have been devoted in recent years to semigroup theory applied to many types of problems. The book under review tries to answer some of the most important questions which arise in the above problems ... . The references are very detailed ... . the very accurate proofs of the theorems and the choices of the examples and applications make it quite readable. In my opinion, it is a very interesting and useful tool for both pure and applied mathematicians." (Silvia Totaro, Mathematical Reviews, Issue 2006 i)"This book is a self-contained mathematical monograph devoted to the theory of semigroups of linear operators ... . The book includes a systematic treatment of classical and recent results in this area as well as a comprehensive survey of the vast literature ... . Each chapter contains a preliminary section with clear references to the bibliography and with technical remarks. ... Throughout the book, the style is clear and elegant. ... this book can be highly recommended to anybody who works in this area." (Adina Luminita Sasu, Zentralblatt MATH, Vol. 1097 (23), 2006)"More precisely, as correctly described in the title, [BA] concentrates on the perturbation of positive semigroups and its applications to birth and death processes, fragmentation processes ... and to kinetic theory. ... Obviously [BA] should be in the hand of every researcher who is interested in any of these applications. It also seems to be the only book available that deals with relatively bounded positive perturbations of positive semigroups and with general questions of their stochasticity and honesty." (H. R. Thieme, SIAM Review, Vol. 49 (2), 2007)

From the reviews:



"Several books of different sorts have been devoted in recent years to semigroup theory applied to many types of problems. The book under review tries to answer some of the most important questions which arise in the above problems ... . The references are very detailed ... . the very accurate proofs of the theorems and the choices of the examples and applications make it quite readable. In my opinion, it is a very interesting and useful tool for both pure and applied mathematicians." (Silvia Totaro, Mathematical Reviews, Issue 2006 i)

"This book is a self-contained mathematical monograph devoted to the theory of semigroups of linear operators ... . The book includes a systematic treatment of classical and recent results in this area as well as a comprehensive survey of the vast literature ... . Each chapter contains a preliminary section with clear references to the bibliography and with technical remarks. ... Throughout the book, the style is clear and elegant. ... this book can be highly recommended to anybody who works in this area." (Adina Luminita Sasu, Zentralblatt MATH, Vol. 1097 (23), 2006)

"More precisely, as correctly described in the title, [BA] concentrates on the perturbation of positive semigroups and its applications to birth and death processes, fragmentation processes ... and to kinetic theory. ... Obviously [BA] should be in the hand of every researcher who is interested in any of these applications. It also seems to be the only book available that deals with relatively bounded positive perturbations of positive semigroups and with general questions of their stochasticity and honesty." (H. R. Thieme, SIAM Review, Vol. 49 (2), 2007)