Harmonic Analysis For Anisotropic Random Walks On Homogeneous Trees

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Harmonic Analysis for Anisotropic Random Walks on Homogeneous Trees

Alessandro Figà-Talamanca,Tim Steger
Harmonic Analysis for Anisotropic Random Walks on Homogeneous Trees Book PDF

Author : Alessandro Figà-Talamanca,Tim Steger
Publisher : American Mathematical Soc.
Page : 68 pages
File Size : 50,6 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825945

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Harmonic Analysis for Anisotropic Random Walks on Homogeneous Trees by Alessandro Figà-Talamanca,Tim Steger Pdf

This work presents a detailed study of the anisotropic series representations of the free product group $\mathbf Z/2\mathbf Z\star \cdots \star \mathbf Z/2\mathbf Z$. 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

M.A. Picardello
Harmonic Analysis and Discrete Potential Theory Book PDF

Author : M.A. Picardello
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 49,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781489923233

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Harmonic Analysis and Discrete Potential Theory by M.A. Picardello Pdf

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

Anatole Katok,Yakov Pesin,Federico Rodriguez Hertz
Modern Theory of Dynamical Systems A Tribute to Dmitry Victorovich Anosov Book PDF

Author : Anatole Katok,Yakov Pesin,Federico Rodriguez Hertz
Publisher : American Mathematical Soc.
Page : 320 pages
File Size : 53,9 Mb
Release : 2017-06-19
Category : Boundary value problems
ISBN : 9781470425609

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Modern Theory of Dynamical Systems: A Tribute to Dmitry Victorovich Anosov by Anatole Katok,Yakov Pesin,Federico Rodriguez Hertz Pdf

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

Wolfgang Woess
Random Walks on Infinite Graphs and Groups Book PDF

Author : Wolfgang Woess
Publisher : Cambridge University Press
Page : 350 pages
File Size : 48,6 Mb
Release : 2000-02-13
Category : Mathematics
ISBN : 9780521552929

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Random Walks on Infinite Graphs and Groups by Wolfgang Woess Pdf

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

Svante Janson
Orthogonal Decompositions and Functional Limit Theorems for Random Graph Statistics Book PDF

Author : Svante Janson
Publisher : American Mathematical Soc.
Page : 78 pages
File Size : 53,6 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825952

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Orthogonal Decompositions and Functional Limit Theorems for Random Graph Statistics by Svante Janson Pdf

This book develops a method to obtain limit theorems for various functionals of random graphs. The method is based on a certain orthogonal decomposition. Janson's results include limit theorems for the two standard random graph models, $G_{n,p}$ and $G_{n,m}$, as well as functional limit theorems for the evolution of a random graph and results on the maximum of a function during the evolution. Janson obtains both normal and nonnormal limits, and the method provides an explanation for the appearance of nonnormal limits. Applications to subgraph counts and to vertex degrees are presented as examples.

On Finite Groups and Homotopy Theory

Ran Levi
On Finite Groups and Homotopy Theory Book PDF

Author : Ran Levi
Publisher : American Mathematical Soc.
Page : 100 pages
File Size : 48,8 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821804018

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On Finite Groups and Homotopy Theory by Ran Levi Pdf

Let $p$ be a fixed prime number. Let $G$ denote a finite $p$-perfect group. This book looks at the homotopy type of the $p$-completed classifying space $BG_p$, where $G$ is a finite $p$-perfect group. The author constructs an algebraic analog of the Quillen's ``plus'' construction for differential graded coalgebras. This construction is used to show that given a finite $p$-perfect group $G$, the loop spaces $BG_p$ admits integral homology exponents. Levi gives examples to show that in some cases our bound is best possible. It is shown that in general $B\ast _p$ admits infinitely many non-trivial $k$-invariants. The author presents examples where homotopy exponents exist. Classical constructions in stable homotopy theory are used to show that the stable homotopy groups of these loop spaces also have exponents.

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

A. L. Levin,Doron Shaul Lubinsky
Christoffel Functions and Orthogonal Polynomials for Exponential Weights on 1 1 Book PDF

Author : A. L. Levin,Doron Shaul Lubinsky
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 44,8 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825990

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Christoffel Functions and Orthogonal Polynomials for Exponential Weights on $[-1, 1]$ by A. L. Levin,Doron Shaul Lubinsky Pdf

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 $[-1,1]$. Levin and Lubinsky obtain such bounds for weights that vanish strongly at 1 and $-1$. They also present uniform estimates of spacing of zeros of orthogonal polynomials and applications to weighted approximation theory.

Classification of Direct Limits of Even Cuntz-Circle Algebras

Huaxin Lin,Norman Christopher Phillips
Classification of Direct Limits of Even Cuntz Circle Algebras Book PDF

Author : Huaxin Lin,Norman Christopher Phillips
Publisher : American Mathematical Soc.
Page : 116 pages
File Size : 48,5 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821804032

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Classification of Direct Limits of Even Cuntz-Circle Algebras by Huaxin Lin,Norman Christopher Phillips Pdf

does not need NBB copy.

Solution of the Truncated Complex Moment Problem for Flat Data

Raúl E. Curto,Lawrence A. Fialkow
Solution of the Truncated Complex Moment Problem for Flat Data Book PDF

Author : Raúl E. Curto,Lawrence A. Fialkow
Publisher : American Mathematical Soc.
Page : 52 pages
File Size : 40,6 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804858

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Solution of the Truncated Complex Moment Problem for Flat Data by Raúl E. Curto,Lawrence A. Fialkow Pdf

In this book, the authors 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 $z$ and $\bar z$ of highest degree can be written in terms of monomials of lower degree. Necessary and sufficient conditions for the existence and uniqueness of representing measures are obtained in terms of positivity and extension criteria for moment matrices.

Molecular Propagation through Electron Energy Level Crossings

George Allan Hagedorn
Molecular Propagation through Electron Energy Level Crossings Book PDF

Author : George Allan Hagedorn
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 50,9 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821826058

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Molecular Propagation through Electron Energy Level Crossings by George Allan Hagedorn Pdf

The principal results of this paper involve the extension of the time-dependent Born-Oppenheimer approximation to accommodate the propagation of nuclei through generic, minimal multiplicity electron energy level crossings. The Born-Oppenheimer approximation breaks down at electron energy level crossings, which are prevalent in molecular systems. We classify generic, minimal multiplicity level crossings and derives a normal form for the electron Hamiltonian near each type of crossing. We then extend the time-dependent Born-Oppenheimer approximation to accommodate the propagation of nuclei through each type of electron energy level crossing.

Excluding Infinite Clique Minors

Neil Robertson,Paul D. Seymour,Robin Thomas
Excluding Infinite Clique Minors Book PDF

Author : Neil Robertson,Paul D. Seymour,Robin Thomas
Publisher : American Mathematical Soc.
Page : 103 pages
File Size : 47,6 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821804025

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Excluding Infinite Clique Minors by Neil Robertson,Paul D. Seymour,Robin Thomas Pdf

Two of the authors proved a well-known conjecture of K. Wagner, that in any infinite set of finite graphs there are two graphs so that one is a minor of the other. A key lemma was a theorem about the structure of finite graphs that have no $K_n$ minor for a fixed integer $n$. Here, the authors obtain an infinite analog of this lemma--a structural condition on a graph, necessary and sufficient for it not to contain a $K_n$ minor, for any fixed infinite cardinal $n$.

Anticipative Girsanov Transformations and Skorohod Stochastic Differential Equations

Rainer Buckdahn
Anticipative Girsanov Transformations and Skorohod Stochastic Differential Equations Book PDF

Author : Rainer Buckdahn
Publisher : American Mathematical Soc.
Page : 88 pages
File Size : 45,6 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821825969

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Anticipative Girsanov Transformations and Skorohod Stochastic Differential Equations by Rainer Buckdahn Pdf

This book presents a survey of some recent developments in an important subfield of the new subject of anticipative stochastic analysis. D. Nualart and E. Pardoux have developed into a practicable calculus the theory of stochastic integration of processes not necessarily adapted to the driving Wiener process. This leads to anticipative stochastic differential equations with Skorohod integral and to anticipative Girsanov transformations, both of which are studied in the present work. The anticipative Girsanov transformations constitute the main tool for tackling stochastic differential equations with Skorohod integral. However, Buckdahn does not restrict attention only to this aspect but also considers different types of anticipative transformations and derives sufficient conditions for their absolute continuity with respect to the Wiener measure. The stochastic differential equations with Skorohod integral are studied under random initial conditions as well as under random boundary conditions.

Triangular Algebras and Ideals of Nest Algebras

John Lindsay Orr
Triangular Algebras and Ideals of Nest Algebras Book PDF

Author : John Lindsay Orr
Publisher : American Mathematical Soc.
Page : 49 pages
File Size : 43,5 Mb
Release : 1995
Category : Mathematics
ISBN : 9780821804056

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Triangular Algebras and Ideals of Nest Algebras by John Lindsay Orr Pdf

Triangular algebras and nest algebras are two important classes of non-selfadjoint operator algebras. In this book, the author uses the new depth of understanding which the similarity theory for nests has opened up to study ideals of nest algebras. In particular, a unique largest diagonal-disjoint ideal is identified for each nest algebra. Using a construction proposed by Kadison and Singer, this ideal can be used to construct new maximal triangular algebras. These new algebras are the first concrete descriptions of maximal triangular algebras that are not nest algebras.

Shortest Paths for Sub-Riemannian Metrics on Rank-Two Distributions

Wensheng Liu,Hector J. Sussmann
Shortest Paths for Sub Riemannian Metrics on Rank Two Distributions Book PDF

Author : Wensheng Liu,Hector J. Sussmann
Publisher : American Mathematical Soc.
Page : 121 pages
File Size : 52,5 Mb
Release : 1995
Category : Extremal problems (Mathematics)
ISBN : 9780821804049

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Shortest Paths for Sub-Riemannian Metrics on Rank-Two Distributions by Wensheng Liu,Hector J. Sussmann Pdf

A sub-Riemannian manifold ([italic capitals]M, E, G) consists of a finite-dimensional manifold [italic capital]M, a rank-two bracket generating distribution [italic capital]E on [italic capital]M, and a Riemannian metric [italic capital]G on [italic capital]E. All length-minimizing arcs on ([italic capitals]M, E, G) are either normal extremals or abnormal extremals. Normal extremals are locally optimal, i.e., every sufficiently short piece of such an extremal is a minimizer. The question whether every length-minimizer is a normal extremal was recently settled by R. G. Montgomery, who exhibited a counterexample. The present work proves that regular abnormal extremals are locally optimal, and, in the case that [italic capital]E satisfies a mild additional restriction, the abnormal minimizers are ubiquitous rather than exceptional. All the topics of this research report (historical notes, examples, abnormal extremals, Hamiltonians, nonholonomic distributions, sub-Riemannian distance, the relations between minimality and extremality, regular abnormal extremals, local optimality of regular abnormal extremals, etc.) are presented in a very clear and effective way.