Sampling theorems associated with singular \(q\)-Sturm Liouville problems

DOI10.1007/s00025-011-0134-9zbMath1264.94082OpenAlexW2473059478MaRDI QIDQ692510

M. C. Fu

Publication date: 6 December 2012

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-011-0134-9

zbMATH Keywords

sampling theorythird Jackson \(q\)-Bessel functionsingular \(q\)-Sturm-Liouville equations

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Sampling theory in information and communication theory (94A20)

Related Items (8)

Variations around a general quantum operator ⋮ q−Hamiltonian systems ⋮ Hermite-Hadamard inequalities for quantum integrals: a unified approach ⋮ Unnamed Item ⋮ Basic Fourier transform on the space of entire functions of logarithm order 2 ⋮ A completeness theorem for a Hahn-Fourier system and an associated classical sampling theorem ⋮ Aβ-Sturm–Liouville problem associated with the general quantum operator ⋮ Sampling theorems for Jackson-Nörlund transforms associated with Hahn-difference operators

Cites Work

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• Linear \(q\)-difference equations
• q-Titchmarsh-Weyl theory: series expansion
• A 𝑞-sampling theorem related to the 𝑞-Hankel transform
• On Lagrange Interpolation and Kramer-Type Sampling Theorems Associated with Sturm–Liouville Problems
• Sampling theorems associated with biorthogonalq-Bessel functions
• On integral transforms whose kernels are solutions of singular Sturm–Liouville problems
• An Addition Theorem and Some Product Formulas for the Hahn-Exton q-Bessel Functions
• Functions 𝑞-orthogonal with respect to their own zeros
• Sampling theory associated withq-difference equations of the Sturm–Liouville type
• On the Uniqueness of the Green's Function Associated with a Second-order Differential Equation
• Beiträge zur Theorie der Heineschen Reihen. Die 24 Integrale der hypergeometrischen q‐Differenzengleichung. Das q‐Analogon der Laplace‐Transformation

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