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

DOI10.1063/1.1794842zbMath1064.42014arXivmath/0311055OpenAlexW2130875730MaRDI QIDQ3024110

Bernhard Beckermann, Evguenii A. Rakhmanov, Andrei Martínez-Finkelshtein, Franck Wielonsky

Publication date: 30 June 2005

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0311055

zbMATH Keywords

orthogonal polynomialsSzegő classBernstein classentropy integral

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Related Items (6)

Discrete entropies of orthogonal polynomials ⋮ Shannon entropy of symmetric Pollaczek polynomials ⋮ Orthogonal polynomials on the circle for the weight \(w\) satisfying conditions \(w,w^{-1}\in \mathrm{BMO}\) ⋮ On the growth of the polynomial entropy integrals for measures in the Szegő class ⋮ On a problem by Steklov ⋮ Asymptotics of orthogonal polynomial's entropy

Cites Work

• Necessary conditions for weighted mean convergence of Fourier series in orthogonal polynomials
• Information entropy of classical orthogonal polynomials and their application to the harmonic oscillator and Coulomb potentials
• Asymptotics for entropy integrals associated with exponential weights
• Sum rules for Jacobi matrices and their applications to spectral theory
• ON THE ASYMPTOTICS OF THE RATIO OF ORTHOGONAL POLYNOMIALS
• Entropic integrals of hyperspherical harmonics and spatial entropy of D-dimensional central potentials
• ASYMPTOTIC BEHAVIOR OF THEL^p-NORMS AND THE ENTROPY FOR GENERAL ORTHOGONAL POLYNOMIALS
• Quantum information entropies and orthogonal polynomials

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