Evolution Processes and the Feynman-Kac Formula / Edition 1

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The evolution of a physical system can often be described in terms of a semigroup of linear operators. Observations of the system may be modelled by a spectral measure. A combination of these basic objects produces a family of operator valued set functions, by which perturbations of the evolution are represented as path integrals. In this book, random processes measured by operator valued set functions - evolution processes - are systematically examined for the first time. The Feynman-Kac formula, representing perturbations of the heat semigroup in terms of integrals with respect to Wiener measure, is extended in a number of directions: to other countably additive processes, not necessarily associated with a probability measure; to unbounded processes such as those associated with Feynman integrals; and to random evolutions.
Audience: Researchers in mathematical physics, functional analysis and shastic processes.

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Editorial Reviews

An advanced mathematical exploration of integration theory in vector spaces connected to a specific application--the representation of evolutions by functional integrals. The specific topics include: vector measures and function spaces, evolution processes, Feynman-Kac Formulae, bilinear integration, random evolutions, bounded evolution processes, integration and unbounded set functions, the Schrodinger Process, and the Radial Dirac Process. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9789048146505
  • Publisher: Springer Netherlands
  • Publication date: 12/6/2010
  • Series: Mathematics and Its Applications (closed) Series , #353
  • Edition description: Softcover reprint of hardcover 1st ed. 1996
  • Edition number: 1
  • Pages: 235
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.53 (d)

Table of Contents

Preface. Introduction. 1. Vector Measures and Function Spaces. 2. Evolution Processes. 3. Feynman-Kac Formulae. 4. Bilinear Integration. 5. Random Evolutions. 6. Some Bounded Evolution Processes. 7. Integration with Respect to Unbounded Set Functions. 8. The Schrödinger Process. 9. The Radial Dirac Process. Bibliography. Index.

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