Basic Fourier series on a \(q\)-linear grid: convergence theorems

DOI10.1016/J.JMAA.2005.10.043zbMath1107.33016OpenAlexW1983091534MaRDI QIDQ852739

José Luis Cardoso

Publication date: 15 November 2006

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2005.10.043

zbMATH Keywords

convergence theorems\(q\)-Fourier series\(q\)-trigonometric functions

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) General harmonic expansions, frames (42C15) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Applications of basic hypergeometric functions (33D90)

Related Items (7)

Variations around a general quantum operator ⋮ Hermite-Hadamard inequalities for quantum integrals: a unified approach ⋮ Uniform convergence of basic Fourier-Bessel series on a \(q\)-linear grid ⋮ Basic Fourier series: convergence on and outside the \(q\)-linear grid ⋮ Aβ-Sturm–Liouville problem associated with the general quantum operator ⋮ On basic Fourier-Bessel expansions ⋮ A few properties of the third Jackson \(q\)-Bessel function

Cites Work

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• 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
• On the zeros of the Hahn-Exton \(q\)-Bessel function and associated \(q\)- Lommel polynomials
• The roots of the third J. Jckson \(q\)-Bessel function
• An introduction to basic Fourier series
• Recurrence relations for the coefficients of the Fourier series expansions with respect to q-classical orthogonal polynomials
• POINTWISE CONVERGENCE OF FOURIER SERIES
• An Addition Theorem and Some Product Formulas for the Hahn-Exton q-Bessel Functions
• The theory of difference analogues of special functions of hypergeometric type
• On the connection and linearization problem for discrete hypergeometric \(q\)-polynomials
• Basic analog of Fourier series on a \(q\)-linear grid.

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