Titchmarsh–Weyl theory for q-Dirac systems

DOI10.1142/S0219025719500103zbMath1425.39008OpenAlexW2958944344MaRDI QIDQ5234906

Hüseyin Tuna, Bilender P. Allahverdiev

Publication date: 7 October 2019

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219025719500103

zbMATH Keywords

singular pointlimit-point caselimit-circle case\(q\)-Dirac operator

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Difference operators (39A70) Difference equations, scaling ((q)-differences) (39A13)

Related Items

q−Hamiltonian systems ⋮ On square integrable solutions of a Hahn-Dirac system

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(q\)-fractional calculus and equations
• Spectral theory of ordinary differential operators
• New \(q\)-derivative and \(q\)-logarithm
• Titchmarsh-Weyl theory for Dirac systems with transmission conditions
• A basic analog of a theorem of Pólya
• Linear \(q\)-difference equations
• Gaussian binomial coefficients
• Another addition theorem for theq-exponential function
• q-Titchmarsh-Weyl theory: series expansion
• Asymptotic formulae for eigenvalues and eigenfunctions of q -Sturm-Liouville problems
• One-dimensional q -Dirac equation
• A completeness relation for the q-analogue coherent states by q-integration
• The Basic Bessel Functions and Polynomials
• Dissipative q-Dirac operator with general boundary conditions
• More on the q-oscillator algebra and q-orthogonal polynomials
• A q deformation of the Gauss distribution
• A model for the continuous q-ultraspherical polynomials
• Beiträge zur Theorie der Heineschen Reihen. Die 24 Integrale der hypergeometrischen q‐Differenzengleichung. Das q‐Analogon der Laplace‐Transformation
• Quantum calculus