Topics in Harmonic Analysis and Ergodic Theory

by Rosenblatt, Joseph M.

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Title Statements

Full title :Topics in Harmonic Analysis and Ergodic Theory.

Edition Statements

Publication Date:2007.

Publication Statements

Publisher(s):American mathematical Society
Place of Publication:Providence
Language:eng
Publication Date:2007.

The Physical Object

Description:1 online resource (242 pages)

Edition Identifiers

ISBN:9780821881231, 082188123X, 9780821842355, 0821842358, 9780821857731, 0821857738
oclc:ocn990589067
LC Classification:QA403 ǂb T567 2007eb
Dewey Decimal:515/.2433

Contents -- Preface -- List of Participants -- Topics in Ergodic Theory and Harmonic Analysis: An Overview -- The mathematical work of Roger Jones -- The Central Limit Theorem for Random Walks on Orbits of Probability Preserving Transformations -- Probability, Ergodic Theory, and Low-Pass Filters -- (1) Introduction. An overview. Basic notation -- (2) Two simple examples: the Haar function and the stretched Haar function. Correcting defective filters -- (3) An outline of the probability argument: Low-pass filters as transition probabilities and a zero-one principle

(4) The Paul LÃ©vy Borel-Cantelli Lemma and the convergence/divergence of an infinite product(5) Doeblin's coupling for low-pass filters -- (6) The state space and the path space. Basic probability theory for this application -- (7) Coding R1 into the state space: The signed magnitude representation versus the two's complement representation -- (8) The construction of a stationary Markov process. P-invariant measures, martingales, and harmonic functions -- (9) The crux of the problem: Invariant sets. Cycles and perfect sets. Forbidden zeros

(10) The asymptotic behavior of paths from an initial point. Recurrent and tra…

Subjects

Analyse harmonique -- Congrès. -- Infor… Conference papers and proceedings Ergodic theory Ergodic theory -- Congresses Géométrie -- Congrès geometry Geometry -- Congresses Harmonic analysis -- Congresses. -- Dat… Théorie ergodique -- Congrès