Non-Autonomous Kato Classes and Feynman-Kac Propagators

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9789812565570: Non-Autonomous Kato Classes and Feynman-Kac Propagators

"This book is a very welcome contribution to the growing literature on this fascinating field ... It is clearly written and therefore accessible to graduate students and researchers with a solid background in analysis ... It will certainly attract many new researchers to a field which had, curiously, a very slow start but seems now ready to reach its maturity, both on the theoretical and applied sides."Mathematical Reviews

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This book provides an introduction to propagator theory. Propagators, or evolution families, are two-parameter analogues of semigroups of operators. Propagators are encountered in analysis, mathematical physics, partial differential equations, and probability theory. They are often used as mathematical models of systems evolving in a changing environment. A unifying theme of the book is the theory of Feynman-Kac propagators associated with time-dependent measures from non-autonomous Kato classes. In applications, a Feynman-Kac propagator describes the evolution of a physical system in the presence of time-dependent absorption and excitation. The book is suitable as an advanced textbook for graduate courses.

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