Author : Joseph Rosenblatt
Publisher : American Mathematical Soc.
Page : 242 pages
File Size : 15,22 MB
Release : 2007
Category : Mathematics
ISBN : 0821842358
There are strong connections between harmonic analysis and ergodic theory. A recent example of this interaction is the proof of the spectacular result by Terence Tao and Ben Green that the set of prime numbers contains arbitrarily long arithmetic progressions. This text presents a series of essays on the topic.
Author : Karl Endel Petersen
Publisher : Cambridge University Press
Page : 452 pages
File Size : 35,1 MB
Release : 1995
Category : Ergodic theory
ISBN : 0521459990
Tutorial survey papers on important areas of ergodic theory, with related research papers.
Author : Harry Furstenberg
Publisher : Princeton University Press
Page : 216 pages
File Size : 41,95 MB
Release : 2014-07-14
Category : Mathematics
ISBN : 1400855160
Topological dynamics and ergodic theory usually have been treated independently. H. Furstenberg, instead, develops the common ground between them by applying the modern theory of dynamical systems to combinatories and number theory. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author : Roger E. Howe
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 20,33 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461392004
This book mainly discusses the representation theory of the special linear group 8L(2, 1R), and some applications of this theory. In fact the emphasis is on the applications; the working title of the book while it was being writ ten was "Some Things You Can Do with 8L(2). " Some of the applications are outside representation theory, and some are to representation theory it self. The topics outside representation theory are mostly ones of substantial classical importance (Fourier analysis, Laplace equation, Huyghens' prin ciple, Ergodic theory), while the ones inside representation theory mostly concern themes that have been central to Harish-Chandra's development of harmonic analysis on semisimple groups (his restriction theorem, regularity theorem, character formulas, and asymptotic decay of matrix coefficients and temperedness). We hope this mix of topics appeals to nonspecialists in representation theory by illustrating (without an interminable prolegom ena) how representation theory can offer new perspectives on familiar topics and by offering some insight into some important themes in representation theory itself. Especially, we hope this book popularizes Harish-Chandra's restriction formula, which, besides being basic to his work, is simply a beautiful example of Fourier analysis on Euclidean space. We also hope representation theorists will enjoy seeing examples of how their subject can be used and will be stimulated by some of the viewpoints offered on representation-theoretic issues.
Author : Tullio Ceccherini-Silberstein
Publisher : Cambridge University Press
Page : 589 pages
File Size : 47,22 MB
Release : 2018-06-21
Category : Mathematics
ISBN : 1107182336
A self-contained introduction to discrete harmonic analysis with an emphasis on the Discrete and Fast Fourier Transforms.
Author : Eli Glasner
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 49,5 MB
Release : 2015-01-09
Category : Mathematics
ISBN : 1470419513
This book introduces modern ergodic theory. It emphasizes a new approach that relies on the technique of joining two (or more) dynamical systems. This approach has proved to be fruitful in many recent works, and this is the first time that the entire theory is presented from a joining perspective. Another new feature of the book is the presentation of basic definitions of ergodic theory in terms of the Koopman unitary representation associated with a dynamical system and the invariant mean on matrix coefficients, which exists for any acting groups, amenable or not. Accordingly, the first part of the book treats the ergodic theory for an action of an arbitrary countable group. The second part, which deals with entropy theory, is confined (for the sake of simplicity) to the classical case of a single measure-preserving transformation on a Lebesgue probability space.
Author : Yitzhak Katznelson
Publisher :
Page : 292 pages
File Size : 21,5 MB
Release : 1968
Category : Harmonic analysis
ISBN :
Author : Béla Sz Nagy
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 38,97 MB
Release : 2010-09-01
Category : Mathematics
ISBN : 1441960937
The existence of unitary dilations makes it possible to study arbitrary contractions on a Hilbert space using the tools of harmonic analysis. The first edition of this book was an account of the progress done in this direction in 1950-70. Since then, this work has influenced many other areas of mathematics, most notably interpolation theory and control theory. This second edition, in addition to revising and amending the original text, focuses on further developments of the theory, including the study of two operator classes: operators whose powers do not converge strongly to zero, and operators whose functional calculus (as introduced in Chapter III) is not injective. For both of these classes, a wealth of material on structure, classification and invariant subspaces is included in Chapters IX and X. Several chapters conclude with a sketch of other developments related with (and developing) the material of the first edition.
Author : A.A. Tempelman
Publisher : Springer Science & Business Media
Page : 418 pages
File Size : 20,7 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 9401714606
This 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.
Author : Michael C. Fu
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 11,70 MB
Release : 2007-06-22
Category : Business & Economics
ISBN : 0817645454
This self-contained volume brings together a collection of chapters by some of the most distinguished researchers and practitioners in the field of mathematical finance and financial engineering. Presenting state-of-the-art developments in theory and practice, the book has real-world applications to fixed income models, credit risk models, CDO pricing, tax rebates, tax arbitrage, and tax equilibrium. It is a valuable resource for graduate students, researchers, and practitioners in mathematical finance and financial engineering.
