The \(q\)-cosine Fourier transform and the \(q\)-heat equation

DOI10.1007/s11139-012-9412-8zbMath1255.33009OpenAlexW1995273417MaRDI QIDQ693022

Fethi Bouzeffour, Ahmed Fitouhi

Publication date: 7 December 2012

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-012-9412-8

zbMATH Keywords

basic hypergeometric integralsbasic orthogonal polynomials and functions

Mathematics Subject Classification ID

Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Basic hypergeometric integrals and functions defined by them (33D60)

Related Items (11)

Sobolev type spaces in quantum calculus ⋮ On Nash and Carlson's inequalities for symmetric \(q\)-integral transforms ⋮ Inversion formulas for \(q\)-Riemann-Liouville and \(q\)-Weyl transforms ⋮ Applications of the Mellin transform in quantum calculus ⋮ On a \(q\)-Paley--Wiener theorem ⋮ A variation of the Lq,p‐uncertainty inequalities of Heisenberg‐type for symmetric q‐integral transforms ⋮ On the heat and wave equations with the Sturm-Liouville operator in quantum calculus ⋮ A characterization of weighted Besov spaces in quantum calculus ⋮ The \textit{q-j}\(_\alpha\) Bessel function ⋮ On the generalized Hilbert transform and weighted Hardy spaces in \(q\)-Dunkl harmonic analysis ⋮ q-Littlewood-Paley g-function

Cites Work

• Heat ``polynomials for a singular differential operator on (0,\(\infty)\)
• Elements of q-harmonic analysis
• The q-analogue of the Laguerre polynomials
• Expansions in Terms of Heat Polynomials and Associated Functions
• On q-Analogues of the Fourier and Hankel Transforms
• Shorter Notes: A Simple Proof of Ramanujan's 1 Ψ 1 Sum
• The Generalized Double Pendulum
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The \(q\)-cosine Fourier transform and the \(q\)-heat equation