A Right Inverse of the Askey-Wilson Operator

DOI10.2307/2160942zbMath0828.33013arXivmath/9310219OpenAlexW2950539622MaRDI QIDQ4845930

B. Malcolm Brown, Mourad E. H. Ismail

Publication date: 21 August 1995

Full work available at URL: https://arxiv.org/abs/math/9310219

zbMATH Keywords

\(q\)-seriestheta functiondivided difference operator

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45)

Related Items

Askey–Wilson operator on entire functions of exponential type ⋮ Special nonuniform lattice (snul) orthogonal polynomials on discrete dense sets of points ⋮ \(q\)-fractional integral operators with two parameters ⋮ An inverse to the Askey-Wilson operator. ⋮ A new approach to the theory of classical hypergeometric polynomials ⋮ A Bernstein type inequality for the Askey-Wilson operator ⋮ Nevanlinna theory of the Askey-Wilson divided difference operator ⋮ Fractional powers of a difference operator ⋮ A moment problem and a family of integral evaluations ⋮ \(q\)-fractional Askey-Wilson integrals and related semigroups of operators ⋮ Inverse operators, \(q\)-fractional integrals, and \(q\)-Bernoulli polynomials

Cites Work

• The zeros of basic Bessel functions, the functions J(nu+ax)(x), and associated orthogonal polynomials
• Diagonalization of certain integral operators
• Diagonalization of certain integral operators. II
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
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