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Invariant Measures

Author: John Von Neumann

Publisher: American Mathematical Soc.

ISBN:

Category: Mathematics

Page: 134

View: 820

This is a heretofore unpublished set of lecture notes by the late John von Neumann on invariant measures, including Haar measures on locally compact groups. The notes for the first half of the book have been prepared by Paul Halmos. The second half of the book includes a discussion of Kakutani's very interesting approach to invariant measures.

Invariant Measures for Unitary Groups Associated to Kac-Moody Lie Algebras

Author: Doug Pickrell

Publisher: American Mathematical Soc.

ISBN:

Category: Mathematics

Page: 125

View: 974

The main purpose of this paper is to prove the existence, and in some cases the uniqueness, of unitarily invariant measures on formal completions of groups associated to affine Kac-Moody algebras, and associated homogeneous spaces. The basic invariant measure is a natural generalization of Haar measure for a simply connected compact Lie group, and its projection to flag spaces is a generalization of the normalized invariant volume element. The other 'invariant measures' are actually measures having values in line bundles over these spaces; these bundle-valued measures heuristically arise from coupling the basic invariant measure to Hermitian structures on associated line bundles, but in this infinite dimensional setting they are generally singular with respect to the basic invariant measure.

Exposed Points of Convex Sets and Weak Sequential Convergence

Applications to Invariant Means, to Existence of Invariant Measures for a Semigroup of Markov Operators Etc ...

Author: Edmond E. Granirer

Publisher: American Mathematical Soc.

ISBN:

Category: Mathematics

Page: 80

View: 498

Dynamics in One Non-Archimedean Variable

Author: Robert L. Benedetto

Publisher: American Mathematical Soc.

ISBN:

Category: Analytic spaces

Page: 463

View: 328

The theory of complex dynamics in one variable, initiated by Fatou and Julia in the early twentieth century, concerns the iteration of a rational function acting on the Riemann sphere. Building on foundational investigations of p-adic dynamics in the late twentieth century, dynamics in one non-archimedean variable is the analogous theory over non-archimedean fields rather than over the complex numbers. It is also an essential component of the number-theoretic study of arithmetic dynamics. This textbook presents the fundamentals of non-archimedean dynamics, including a unified exposition of Rivera-Letelier's classification theorem, as well as results on wandering domains, repelling periodic points, and equilibrium measures. The Berkovich projective line, which is the appropriate setting for the associated Fatou and Julia sets, is developed from the ground up, as are relevant results in non-archimedean analysis. The presentation is accessible to graduate students with only first-year courses in algebra and analysis under their belts, although some previous exposure to non-archimedean fields, such as the p-adic numbers, is recommended. The book should also be a useful reference for more advanced students and researchers in arithmetic and non-archimedean dynamics.

Bulletin (new series) of the American Mathematical Society

Author: American Mathematical Society

Publisher:

ISBN:

Category: Mathematics

Page:

View: 347

Finitary Measures for Subshifts of Finite Type and Sofic Systems

Author: Bruce Kitchens

Publisher: American Mathematical Soc.

ISBN:

Category: Mathematics

Page: 68

View: 446

Conditional Stability and Real Analytic Pseudo-Anosov Maps

Author: Marlies Gerber

Publisher: American Mathematical Soc.

ISBN:

Category: Mathematics

Page: 116

View: 837

Memoirs of the American Mathematical Society

Author:

Publisher:

ISBN:

Category: Mathematics

Page:

View: 934

American Book Publishing Record

Author:

Publisher:

ISBN:

Category: American literature

Page:

View: 913

Notices of the American Mathematical Society

Author: American Mathematical Society

Publisher:

ISBN:

Category: Mathematics

Page:

View: 965

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