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Topics in harmonic analysis and ergodic theory : December 2-4, 2005, DePaul University, Chicago, Illinois / Joseph M. Rosenblatt, Alexander M. Stokolos, Ahmed I. Zayed, editors.
- Format:
- Book
- Series:
- Contemporary mathematics (American Mathematical Society) ; v. 444.
- Contemporary mathematics, 0271-4132 ; volume 444
- Language:
- English
- Subjects (All):
- Harmonic analysis--Congresses.
- Harmonic analysis.
- Ergodic theory--Congresses.
- Ergodic theory.
- Geometry--Data processing--Congresses.
- Geometry.
- Physical Description:
- 1 online resource (242 p.)
- Edition:
- 1st ed.
- Place of Publication:
- Providence, Rhode Island : American Mathematical Society, [2007]
- Language Note:
- English
- 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""
- ""(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""
- Notes:
- Description based upon print version of record.
- Includes bibliographical references.
- Description based on print version record.
- ISBN:
- 0-8218-8123-X
- 0-8218-4235-8
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