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OverviewThis volume is devoted to generalizations of the classical Birkhoff and von Neuman ergodic theorems to semigroup representations in Banach spaces, semigroup actions in measure spaces, homogeneous random fields and random measures on homogeneous spaces. The ergodicity, mixing and quasimixing of semigroup actions and homogeneous random fields are considered as well. In particular homogeneous spaces, on which all homogeneous random fields are quasimixing are introduced and studied (the n-dimensional Euclidean and Lobachevsky spaces with n>=2, and all simple Lie groups with finite centre are examples of such spaces. Also dealt with are applications of general ergodic theorems for the construction of specific informational and thermodynamical characteristics of homogeneous random fields on amenable groups and for proving general versions of the McMillan, Breiman and Lee-Yang theorems. A variational principle which characterizes the Gibbsian homogeneous random fields in terms of the specific free energy is also proved. The book has eight chapters, a number of appendices and a substantial list of references. For researchers whose works involves probability theory, ergodic theory, harmonic analysis, measure theory and statistical Physics. Full Product DetailsAuthor: A.A. TempelmanPublisher: Springer Imprint: Springer Edition: Softcover reprint of the original 1st ed. 1992 Volume: 78 Dimensions: Width: 15.50cm , Height: 2.10cm , Length: 23.50cm Weight: 0.640kg ISBN: 9789048141555ISBN 10: 9048141559 Pages: 399 Publication Date: 15 December 2010 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of Contents1: Means and averageable functions.- 2: Ergodicity and mixing.- 3: Averaging sequences. Universal ergodic theorems.- 4: Mean ergodic theorems.- 5: Maximal and dominated ergodic theorems.- 6: Pointwise ergodic theorems.- 7: Ergodic theorems for homogeneous random measures.- 8: Specific informational and thermodynamical characteristics of homogeneous random fields.- § 1. Groups and semigroups.- § 2. Homogeneous and group-type homogeneous spaces.- § 3. Amenable semigroups and ergodic nets.- § 4. Positive definite functions.- § 5. Representations of semigroups in Banach spaces.- § 6. Weakly almost periodic elements and functions.- § 7. Dynamical systems.- § 8. Homogeneous random functions.- § 9. Measurability and continuity of representations, dynamical systems and homogeneous random fields.- § 12. The Banach convergence principle.- § 13. Directions and nets.- § 14. Correspondence between “left” and “right” objects and conditions.- References.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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