Search Results: invariant-measures-american-mathematics-society-non-series-title

Invariant Measures

Author: John Von Neumann

Publisher: American Mathematical Soc.

ISBN: 9780821886045

Category: Mathematics

Page: 134

View: 5988

This is a heretofore unpublished set of lecture notes by the late John von Neumann on invariant measures, including Haar measures on locally compact groups.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: 0821820680

Category: Mathematics

Page: 125

View: 4934

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.

Bulletin (new Series) of the American Mathematical Society

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 4718

Discrete Groups, Expanding Graphs and Invariant Measures

Author: Alex Lubotzky

Publisher: Springer Science & Business Media

ISBN: 3034603320

Category: Mathematics

Page: 196

View: 5016

In the last ?fteen years two seemingly unrelated problems, one in computer science and the other in measure theory, were solved by amazingly similar techniques from representation theory and from analytic number theory. One problem is the - plicit construction of expanding graphs («expanders»). These are highly connected sparse graphs whose existence can be easily demonstrated but whose explicit c- struction turns out to be a dif?cult task. Since expanders serve as basic building blocks for various distributed networks, an explicit construction is highly des- able. The other problem is one posed by Ruziewicz about seventy years ago and studied by Banach [Ba]. It asks whether the Lebesgue measure is the only ?nitely additive measure of total measure one, de?ned on the Lebesgue subsets of the n-dimensional sphere and invariant under all rotations. The two problems seem, at ?rst glance, totally unrelated. It is therefore so- what surprising that both problems were solved using similar methods: initially, Kazhdan’s property (T) from representation theory of semi-simple Lie groups was applied in both cases to achieve partial results, and later on, both problems were solved using the (proved) Ramanujan conjecture from the theory of automorphic forms. The fact that representation theory and automorphic forms have anything to do with these problems is a surprise and a hint as well that the two questions are strongly related.

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: 0821818236

Category: Mathematics

Page: 80

View: 2726

The Joys of Haar Measure

Author: Joe Diestel,Angela Spalsbury

Publisher: American Mathematical Soc.

ISBN: 1470409356

Category: Mathematics

Page: 320

View: 2466

From the earliest days of measure theory, invariant measures have held the interests of geometers and analysts alike, with the Haar measure playing an especially delightful role. The aim of this book is to present invariant measures on topological groups, progressing from special cases to the more general. Presenting existence proofs in special cases, such as compact metrizable groups, highlights how the added assumptions give insight into just what the Haar measure is like; tools from different aspects of analysis and/or combinatorics demonstrate the diverse views afforded the subject. After presenting the compact case, applications indicate how these tools can find use. The generalisation to locally compact groups is then presented and applied to show relations between metric and measure theoretic invariance. Steinlage's approach to the general problem of homogeneous action in the locally compact setting shows how Banach's approach and that of Cartan and Weil can be unified with good effect. Finally, the situation of a nonlocally compact Polish group is discussed briefly with the surprisingly unsettling consequences indicated. The book is accessible to graduate and advanced undergraduate students who have been exposed to a basic course in real variables, although the authors do review the development of the Lebesgue measure. It will be a stimulating reference for students and professors who use the Haar measure in their studies and research.

Monographic Series

Author: Library of Congress

Publisher: N.A

ISBN: N.A

Category: Children's literature in series

Page: N.A

View: 2092

An Introduction to Infinite Ergodic Theory

Author: Jon Aaronson

Publisher: American Mathematical Soc.

ISBN: 0821804944

Category: Mathematics

Page: 284

View: 3155

Infinite ergodic theory is the study of measure preserving transformations of infinite measure spaces. The book focuses on properties specific to infinite measure preserving transformations. The work begins with an introduction to basic nonsingular ergodic theory, including recurrence behavior, existence of invariant measures, ergodic theorems, and spectral theory. A wide range of possible ``ergodic behavior'' is catalogued in the third chapter mainly according to the yardsticks of intrinsic normalizing constants, laws of large numbers, and return sequences. The rest of the book consists of illustrations of these phenomena, including Markov maps, inner functions, and cocycles and skew products. One chapter presents a start on the classification theory.

The Knot Book

An Elementary Introduction to the Mathematical Theory of Knots

Author: Colin Conrad Adams

Publisher: American Mathematical Soc.

ISBN: 0821836781

Category: Mathematics

Page: 306

View: 4323

Knots are familiar objects. We use them to moor our boats, to wrap our packages, to tie our shoes. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. The Knot Book is an introduction to this rich theory, starting from our familiar understanding of knots and a bit of college algebra and finishing with exciting topics of current research. The Knot Book is also about the excitement of doing mathematics. Colin Adams engages the reader with fascinating examples, superb figures, and thought-provoking ideas. He also presents the remarkable applications of knot theory to modern chemistry, biology, and physics. This is a compelling book that will comfortably escort you into the marvelous world of knot theory. Whether you are a mathematics student, someone working in a related field, or an amateur mathematician, you will find much of interest in The Knot Book.

American Book Publishing Record

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 8580

Conformally Invariant Processes in the Plane

Author: Gregory F. Lawler

Publisher: American Mathematical Soc.

ISBN: 0821846248

Category: Mathematics

Page: 242

View: 9413

Theoretical physicists have predicted that the scaling limits of many two-dimensional lattice models in statistical physics are in some sense conformally invariant. This belief has allowed physicists to predict many quantities for these critical systems. The nature of these scaling limits has recently been described precisely by using one well-known tool, Brownian motion, and a new construction, the Schramm-Loewner evolution (SLE). This book is an introduction to the conformally invariant processes that appear as scaling limits. The following topics are covered: stochastic integration; complex Brownian motion and measures derived from Brownian motion; conformal mappings and univalent functions; the Loewner differential equation and Loewner chains; the Schramm-Loewner evolution (SLE), which is a Loewner chain with a Brownian motion input; and applications to intersection exponents for Brownian motion. The prerequisites are first-year graduate courses in real analysis, complex analysis, and probability. The book is suitable for graduate students and research mathematicians interested in random processes and their applications in theoretical physics.

Memoirs of the American Mathematical Society

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 1496

Foliations I

Author: Alberto Candel,Lawrence Conlon

Publisher: American Mathematical Soc.

ISBN: 0821808095

Category: Mathematics

Page: 402

View: 2160

This is the first of two volumes on the qualitative theory of foliations. This volume is divided into three parts. It is extensively illustrated throughout and provides a large number of examples. Part 1 is intended as a "primer" in foliation theory. A working knowledge of manifold theory and topology is a prerequisite. Fundamental definitions and theorems are explained to prepare the reader for further exploration of the topic. This section places considerable emphasis on the construction of examples, which are accompanied by many illustrations. Part 2 considers foliations of codimension one. Using very hands-on geometric methods, the path leads to a complete structure theory (the theory of levels), which was established by Conlon along with Cantwell, Hector, Duminy, Nishimori, Tsuchiya, et al. Presented here is the first and only full treatment of the theory of levels in a textbook. Part 3 is devoted to foliations of higher codimension, including abstract laminations (foliated spaces). The treatment emphasizes the methods of ergodic theory: holonomy-invariant measures and entropy. Featured are Sullivan's theory of foliation cycles, Plante's theory of growth of leaves, and the Ghys, Langevin, Walczak theory of geometric entropy. This comprehensive volume has something to offer a broad spectrum of readers: from beginners to advanced students to professional researchers. Packed with a wealth of illustrations and copious examples at varying degrees of difficulty, this highly-accessible text offers the first full treatment in the literature of the theory of levels for foliated manifolds of codimension one. It would make an elegant supplementary text for a topics course at the advanced graduate level. Foliations II is Volume 60 in the AMS in the Graduate Studies in Mathematics series.

An Introduction to Measure Theory

Author: Terence Tao

Publisher: American Mathematical Soc.

ISBN: 0821869191

Category: Mathematics

Page: 206

View: 3104

This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Caratheodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.

Proceedings of the American Mathematical Society

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 2594

Contains the material formerly published in even-numbered issues of the Bulletin of the American Mathematical Society.

Finitary Measures for Subshifts of Finite Type and Sofic Systems

Author: Bruce Kitchens,Selim Tuncel

Publisher: American Mathematical Soc.

ISBN: 082182340X

Category: Mathematics

Page: 68

View: 5436

Notices of the American Mathematical Society

Author: American Mathematical Society

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 5980

Transactions of the American Mathematical Society

Author: American Mathematical Society

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 5949

Abstracts of Papers Presented to the American Mathematical Society

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 433

Winding Around: The Winding Number in Topology, Geometry, and Analysis

Author: John Roe

Publisher: American Mathematical Soc.

ISBN: 1470421984

Category: Algebraic topology

Page: 269

View: 4182

The winding number is one of the most basic invariants in topology. It measures the number of times a moving point P goes around a fixed point Q, provided that P travels on a path that never goes through Q and that the final position of P is the same as its starting position. This simple idea has far-reaching applications. The reader of this book will learn how the winding number can help us show that every polynomial equation has a root (the fundamental theorem of algebra),guarantee a fair division of three objects in space by a single planar cut (the ham sandwich theorem),explain why every simple closed curve has an inside and an outside (the Jordan curve theorem),relate calculus to curvature and the singularities of vector fields (the Hopf index theorem),allow one to subtract infinity from infinity and get a finite answer (Toeplitz operators),generalize to give a fundamental and beautiful insight into the topology of matrix groups (the Bott periodicity theorem). All these subjects and more are developed starting only from mathematics that is common in final-year undergraduate courses.

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