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Topics in Harmonic Analysis and Ergodic Theory.

Author: Joseph M Rosenblatt; Alexander M Stokolos; Ahmed I Zayed
Publisher: Providence : American Mathematical Society, 2007.
Series: Contemporary Mathematics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:

Based on talks delivered by plenary speakers at a conference on Harmonic Analysis and Ergodic Theory (DePaul University, Chicago, December 2-4, 2005), this book presents articles that are devoted to  Read more...

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Genre/Form: Electronic books
Conference papers and proceedings
Congresses
Additional Physical Format: Print version:
Rosenblatt, Joseph M.
Topics in Harmonic Analysis and Ergodic Theory.
Providence : American Mathematical Society, ©2007
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Joseph M Rosenblatt; Alexander M Stokolos; Ahmed I Zayed
ISBN: 9780821881231 082188123X 9780821842355 0821842358 9780821857731 0821857738
OCLC Number: 990589067
Language Note: English.
Description: 1 online resource (242 pages).
Contents: ""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 Lévy 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 transient points. Attractors and inaccessible sets. Examples""""(11) The probabilistic description of low-pass filters (Theorem 11.1)""; ""(12) The polynomial case: Daubechies' filters and the Pascal-Fermat correspondence. Cohen's necessary and sufficient conditions. A zero-one principle (Theorem 12.1)""; ""(13) Analytic conditions for low-pass filters. A class of examples from subshifts of finite type (Theorem 13.1)""; ""(14) Concluding remarks""; ""(15) References"" ""Ergodic Theory on Borel Foliations by Rn and Zn""""Short review of the work of Professor J. Marshall Ash""; ""Uniqueness questions for multiple trigonometric series""; ""1. Introduction""; ""2. Some Cantor-Lebesgue Type Theorems""; ""2.1. Square Summation""; ""2.2. Restrictedly Rectangular Summation""; ""2.3. Unrestrictedly Rectangular Summation""; ""2.4. Spherical Summation""; ""3. A Uniqueness Theorem for Unrestrictedly Rectangular Convergence""; ""4. A Uniqueness Theorem for Spherical Convergence""; ""5. Sets of Uniqueness under Spherical Summation"" ""6. Questions about Square and Restricted Rectangular Uniqueness""""6.1. Three weak theorems""; ""6.2. Some conjectures""; ""6.3. Towards a counterexample""; ""7. Orthogonal Trigonometric Polynomials""; ""References""; ""Smooth interpolation of functions on Rn""; ""Problems in interpolation theory related to the almost everywhere convergence of Fourier series""; ""Lectures on Nehari's Theorem on the Polydisk""; ""The s-function and the exponential integral""
Series Title: Contemporary Mathematics.
Other Titles: Contemporary Mathematics
Contemporary Mathematics, Volume 444
Topics in harmonic analysis and ergodic theory: December 2-4, 2005, DePaul University, Chicago, Illinois

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