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Linear Infinite-Particle Operators
V. A. Malyshev and R. A. Minlos

Translations of Mathematical Monographs
1995; 298 pp; hardcover
Volume: 143
ISBN-10: 0-8218-0283-6
ISBN-13: 978-0-8218-0283-0
List Price: US$125
Member Price: US$100
Order Code: MMONO/143
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The main subject of this book can be viewed in various ways. From the standpoint of functional analysis, it studies spectral properties of a certain class of linear operators; from the viewpoint of probability theory, it is concerned with the analysis of singular Markov processes; and, from the vantage point of mathematical physics, it analyzes the dynamics of equilibrium systems in quantum statistical physics and quantum field theory. Malyshev and Minlos describe two new approaches to the subject which have not been previously treated in monograph form. They also present background material which makes the book accessible and useful to researchers and graduate students working in functional analysis, probability theory, and mathematical physics.


Research mathematicians and graduate students working in functional analysis, probability theory, and mathematical physics.


"What distinguishes [the book] from other existing monograph with similar scope ... is the emphasis it puts on the contribution of the Moscow school, of which the authors are outstanding representatives. It makes readily available to the mathematical physics community first-hand information on a large piece of relevant work ... The elegance and optimal organisation of the exposition in Chapter 3 ... is fully rewarding."

-- Mathematical Reviews

"The contents of the book comprises the material that has not been treated previously in any monographs and the well-known ones as well ... useful for both researchers and graduate students."

-- Zentralblatt MATH

Table of Contents

  • Introduction
  • Extended introduction
  • Construction of a nonequilibrium dynamics
  • Construction of an equilibrium dynamics
  • Spectral analysis of the Euclidean field transfer matrix
  • Asymptotic completeness for interacting fermion systems
  • The method of Bethe-Salpeter kernels (Dyson's equation)
  • Guide to the Literature
  • References
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