A Polynomial-Type Jost Solution and Spectral Properties of a Self-Adjoint Quantum-Difference Operator
In this paper, we find a polynomial-type Jost solution of a self-adjoint q-difference equation of second order. Then we investigate the analytical properties and asymptotic behavior of the Jost solution. We prove that the self-adjoint operator L generated by the q-difference expression of second order has essential spectrum filling the segment [-2√q,2√q], q > 1. Finally, we examine the properties of the eigenvalues of L.
Y. Aygar and M. Bohner, "A Polynomial-Type Jost Solution and Spectral Properties of a Self-Adjoint Quantum-Difference Operator," Complex Analysis and Operator Theory, vol. 10, no. 6, pp. 1171-1180, Birkhäuser Verlag, Aug 2016.
The definitive version is available at https://doi.org/10.1007/s11785-015-0463-x
Mathematics and Statistics
International Standard Serial Number (ISSN)
Article - Journal
© 2016 Birkhäuser Verlag, All rights reserved.
01 Aug 2016