• español
  • English
  • Login
      • español
      • English
    • English 
      • español
      • English
    • Login
    View Item 
    •   riUAL Home
    • Repositorio de la Producción Científica de la Universidad de Almería
    • Departamento de Matemáticas
    • Artículos de revista Dpto. Matemáticas
    • View Item
    •   riUAL Home
    • Repositorio de la Producción Científica de la Universidad de Almería
    • Departamento de Matemáticas
    • Artículos de revista Dpto. Matemáticas
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Asymptotic upper bounds for the entropy of orthogonal polynomials in the Szegő class.

    Files
    0311055v1.pdf (241.3Kb)
    Identifiers
    URI: http://hdl.handle.net/10835/1640
    ISSN: 1089-7658
    Services
    RISMendeley
    Share
    Stadistics
    View Usage Statistics
    Metadata
    Show full item record
    Author/s
    Beckermann, B.; Martínez-Finkelshtein, Andrei; Rakhmanov, Evgenii A.; Wielonsky, F.
    Date
    2004
    Abstract
    We give an asymptotic upper bound as $n\to\infty$ for the entropy integral $$E_n(w)= -\int p_n^2(x)\log (p_n^2(x))w(x)dx,$$ where $p_n$ is the $n$th degree orthonormal polynomial with respect to a weight $w(x)$ on $[-1,1]$ which belongs to the Szeg\H{o} class. We also study two functionals closely related to the entropy integral. First, their asymptotic behavior is completely described for weights $w$ in the Bernstein class. Then, as for the entropy, we obtain asymptotic upper bounds for these two functionals when $w(x)$ belongs to the Szeg\H{o} class. In each case, we give conditions for these upper bounds to be attained.
    Palabra/s clave
    Análisis asintótico
    Polinomios ortogonales
    Variables aleatorias
    Collections
    • Artículos de revista Dpto. Matemáticas [119]

    Browse

    All of riUALCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

    My Account

    Login

    Statistics

    View Usage Statistics

    Of interest

    About the RepositoryCopyright FAQsSelf-archiving instructions

    Autoarchivo policies of publishers

    Indexed in

    Contact Us
    Contact Us