Orthogonality and completeness of \(q\)-Fourier type systems

DOI10.4171/ZAA/1044zbMath0980.42027OpenAlexW2038777126MaRDI QIDQ5949167

Mourad E. H. Ismail

Publication date: 14 November 2001

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/zaa/1044

zbMATH Keywords

completenessorthogonalityLommel polynomialssystem of \(q\)-exponential functions

Mathematics Subject Classification ID

Other functions defined by series and integrals (33E20) Completeness of sets of functions in nontrigonometric harmonic analysis (42C30)

Related Items (8)

On \(q\)-orthogonal polynomials, dual to little and big \(q\)-Jacobi polynomials ⋮ Polynomial solutions of differential-difference equations ⋮ Uniform convergence of basic Fourier-Bessel series on a \(q\)-linear grid ⋮ Zeros of orthogonal polynomials generated by canonical perturbations of measures ⋮ On the \(q\)-translation associated with the Askey-Wilson operator ⋮ A 𝑞-analogue of the Whittaker-Shannon-Kotel’nikov sampling theorem ⋮ Matrix-valued polynomials generated by the scalar-type Rodrigues' formulas ⋮ Inverse operators, \(q\)-fractional integrals, and \(q\)-Bernoulli polynomials

Cites Work

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• On a class of polynomials orthogonal over a denumerable set
• The zeros of basic Bessel functions, the functions J(nu+ax)(x), and associated orthogonal polynomials
• Basic analog of Fourier series on a \(q\)-quadratic grid
• Diagonalization of certain integral operators
• Diagonalization of certain integral operators. II
• Polynomials orthogonal over a denumerable set
• Discrete and continuous boundary problems
• A class of continued fractions
• Recurrence relations, continued fractions, and orthogonal polynomials
• A model for the continuous q-ultraspherical polynomials

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