A moment problem and a family of integral evaluations

DOI10.1090/S0002-9947-05-03785-2zbMath1089.33016OpenAlexW1858458802MaRDI QIDQ5469963

Mourad E. H. Ismail, Jacob Stordal Christiansen

Publication date: 29 May 2006

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-05-03785-2

zbMATH Keywords

integral operatorsBethe Ansatz equationsindeterminate moment problemsAl-Salam-Chihara polynomialsraising and lowering operators\(q^{-1}\)-Hermite polynomialsdivided difference operatorsbiorthogonal rational functions

Mathematics Subject Classification ID

Moment problems (44A60) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Kernel operators (47B34)

Related Items

q-Titchmarsh-Weyl theory: series expansion ⋮ The spectrum of the right inverse of the Dunkl operator ⋮ Inverse of infinite Hankel moment matrices ⋮ Integral and series representations of q-polynomials and functions: Part III theta, Ramanujan and q-Bessel functions ⋮ Indeterminate moment problem associated with continuous dual q-Hahn polynomials ⋮ Spectral properties of a \(q\)-Sturm--Liouville operator ⋮ Constructing measures with identical moments ⋮ Connection relations and characterizations of orthogonal polynomials ⋮ Functions of the second kind for classical polynomials ⋮ Biorthogonal exponential sequences with weight function $\exp(ax^2+ibx)$ on the real line and an orthogonal sequence of trigonometric functions ⋮ Solutions of the Al-Salam–Chihara and allied moment problems

Cites Work

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• More q-beta integrals
• Density questions in the classical theory of moments
• Extremal measures for a system of orthogonal polynomials
• The classical moment problem as a self-adjoint finite difference operator
• An inverse to the Askey-Wilson operator.
• q-Integral and Moment Representations for q-Orthogonal Polynomials
• Recurrence relations, continued fractions, and orthogonal polynomials
• q-Hermite Polynomials, Biorthogonal Rational Functions, and q-Beta Integrals
• Classical Orthogonal Polynomials as Moments
• A Right Inverse of the Askey-Wilson Operator
• q-Hermite Polynomials and Classical Orthogonal Polynomials