Topics in Harmonic Analysis and Ergodic Theory.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Rosenblatt, Joseph M.
Otros Autores: Stokolos, Alexander M., Zayed, Ahmed I.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence : American Mathematical Society, 2007.
Colección:Contemporary Mathematics.
Temas:
Harmonic analysis > Data processing > Congresses.
Ergodic theory > Congresses.
Geometry > Congresses.
Analyse harmonique > Informatique > Congrès.
Théorie ergodique > Congrès.
Géométrie > Congrès.
Ergodic theory
Geometry
Conference papers and proceedings
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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 ZnShort 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 Uniqueness6.1. 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

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