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Harmonic Analysis for Anisotropic Random Walks on Homogeneous Trees

Author: Alessandro Figà-Talamanca

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 86

ISBN-13: 0821825941

This work presents a detailed study of the anisotropic series representations of the free product group Z/2Z*...*Z/2Z. These representations are infinite dimensional, irreducible, and unitary and can be divided into principal and complementary series. Anisotropic series representations are interesting because, while they are not restricted from any larger continuous group in which the discrete group is a lattice, they nonetheless share many properties of such restrictions. The results of this work are also valid for nonabelian free groups on finitely many generators.

Harmonic Analysis and Discrete Potential Theory

Author: M.A. Picardello

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 299

ISBN-13: 1489923233

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This book collects the Proceedings of a Congress held in Frascati (Rome) in the period July 1 -July 10, 1991, on the subject of harmonic analysis and discrete potential theory, and related topics. The Congress was made possible by the financial support of the Italian National Research Council ("Gruppo GNAFA"), the Ministry of University ("Gruppo Analisi Funzionale" of the University of Milano), the University of Rome "Tor Vergata", and was also patronized by the Centro "Vito Volterra" of the University of Rome "Tor Vergata". Financial support for publishing these Proceedings was provided by the University of Rome "Tor Vergata", and by a generous contribution of the Centro "Vito Volterra". I am happy of this opportunity to acknowledge the generous support of all these Institutions, and to express my gratitude, and that of all the participants. A number of distinguished mathematicians took part in the Congress. Here is the list of participants: M. Babillot, F. Choucroun, Th. Coulhon, L. Elie, F. Ledrappier, N. Th. Varopoulos (Paris); L. Gallardo (Brest); Ph. Bougerol, B. Roynette (Nancy); O. Gebuhrer (Strasbourg); G. Ahumada-Bustamante (Mulhouse); A. Valette (Neuchatel); P. Gerl (Salzburg); W. Hansen, H. Leptin (Bielefeld); M. Bozejko, A. Hulanicki, T. Pytlik (Wroclaw); C. Thomassen (Lyngby); P. Sjogren (Goteborg); V. Kaimanovich (Leningrad); A. Nevo (Jerusalem); T. Steger (Chicago); S. Sawyer, M. Taibleson, G. Weiss (St. Louis); J. Cohen, S.S ali ani (Maryland); D. Voiculescu (Berkeley); A. Zemanian (Stony Brook); S. Northshield (Plattsburgh); J. Taylor (Montreal); J

Modern Theory of Dynamical Systems: A Tribute to Dmitry Victorovich Anosov

Author: Anatole Katok

Publisher: American Mathematical Soc.

Published: 2017-06-19

Total Pages: 320

ISBN-13: 1470425602

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This volume is a tribute to one of the founders of modern theory of dynamical systems, the late Dmitry Victorovich Anosov. It contains both original papers and surveys, written by some distinguished experts in dynamics, which are related to important themes of Anosov's work, as well as broadly interpreted further crucial developments in the theory of dynamical systems that followed Anosov's original work. Also included is an article by A. Katok that presents Anosov's scientific biography and a picture of the early development of hyperbolicity theory in its various incarnations, complete and partial, uniform and nonuniform.

Random Walks on Infinite Graphs and Groups

Author: Wolfgang Woess

Publisher: Cambridge University Press

Published: 2000-02-13

Total Pages: 350

ISBN-13: 0521552923

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The main theme of this book is the interplay between the behaviour of a class of stochastic processes (random walks) and discrete structure theory. The author considers Markov chains whose state space is equipped with the structure of an infinite, locally finite graph, or as a particular case, of a finitely generated group. The transition probabilities are assumed to be adapted to the underlying structure in some way that must be specified precisely in each case. From the probabilistic viewpoint, the question is what impact the particular type of structure has on various aspects of the behaviour of the random walk. Vice-versa, random walks may also be seen as useful tools for classifying, or at least describing the structure of graphs and groups. Links with spectral theory and discrete potential theory are also discussed. This book will be essential reading for all researchers working in stochastic process and related topics.

Orthogonal Decompositions and Functional Limit Theorems for Random Graph Statistics

Author: Svante Janson

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 90

ISBN-13: 082182595X

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We define an orthogonal basis in the space of real-valued functions of a random graph, and prove a functional limit theorem for this basis. Limit theorems for other functions then follow by decomposition. The results include limit theorems for the two random graph models [italic]G[subscript italic]n, [subscript italic]p and [italic]G[subscript italic]n, [subscript italic]m as well as functional limit theorems for the evolution of a random graph and results on the maximum of a function during the evolution. Both normal and non-normal limits are obtained. As examples, applications are given to subgraph counts and to vertex degrees.

On Finite Groups and Homotopy Theory

Author: Ran Levi

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 121

ISBN-13: 0821804014

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In part 1 we study the homology, homotopy, and stable homotopy of [capital Greek]Omega[italic capital]B[lowercase Greek]Pi[up arrowhead][over][subscript italic]p, where [italic capital]G is a finite [italic]p-perfect group. In part 2 we define the concept of resolutions by fibrations over an arbitrary family of spaces.

Christoffel Functions and Orthogonal Polynomials for Exponential Weights on $[-1, 1]$

Author: A. L. Levin

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 166

ISBN-13: 0821825992

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Bounds for orthogonal polynomials which hold on the 'whole' interval of orthogonality are crucial to investigating mean convergence of orthogonal expansions, weighted approximation theory, and the structure of weighted spaces. This book focuses on a method of obtaining such bounds for orthogonal polynomials (and their Christoffel functions) associated with weights on [-1,1]. Also presented are uniform estimates of spacing of zeros of orthogonal polynomials and applications to weighted approximation theory.

Compact Connected Lie Transformation Groups on Spheres with Low Cohomogeneity, I

Author: Eldar Straume

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 106

ISBN-13: 082180409X

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The cohomogeneity of a transformation group ([italic capitals]G, X) is, by definition, the dimension of its orbit space, [italic]c = dim [italic capitals]X, G. By enlarging this simple numerical invariant, but suitably restricted, one gradually increases the complexity of orbit structures of transformation groups. This is a natural program for classical space forms, which traditionally constitute the first canonical family of testing spaces, due to their unique combination of topological simplicity and abundance in varieties of compact differentiable transformation groups.

Classification of Direct Limits of Even Cuntz-Circle Algebras

Author: Huaxin Lin

Publisher: American Mathematical Soc.

Published: 1995

Total Pages: 129

ISBN-13: 0821804030

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We prove a classification theorem for purely infinite C∗-algebras that is strong enough to show that the tensor products of two different irrational rotation algebras with the same even Cuntz algebra are isomorphic.

Solution of the Truncated Complex Moment Problem for Flat Data

Author: Raúl E. Curto

Publisher: American Mathematical Soc.

Published: 1996

Total Pages: 69

ISBN-13: 0821804855

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We introduce a matricial approach to the truncated complex moment problem, and apply it to the case of moment matrices of flat data type, for which the columns corresponding to the homogeneous monomials in [italic]z and [italic]z̄ of highest degree can be written in terms of monomials of lower degree. We discuss the connection between complex moment problems and the subnormal completion problem for 2-variable weighted shifts, and present in detail the construction of solutions for truncated complex moment problems associated with monomials of degrees one and two.