Table of Contents
International Journal of Partial Differential Equations
Volume 2014 (2014), Article ID 920695, 6 pages
http://dx.doi.org/10.1155/2014/920695
Research Article

Spectral Bounds for Polydiagonal Jacobi Matrix Operators

Mathematics Department, Imperial College London, South Kensington, 180 Queen’s Gate, London SW7 2AZ, UK

Received 24 April 2014; Accepted 4 September 2014; Published 19 October 2014

Academic Editor: Michael Grinfeld

Copyright © 2014 Arman Sahovic. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The research on spectral inequalities for discrete Schrödinger operators has proved fruitful in the last decade. Indeed, several authors analysed the operator’s canonical relation to a tridiagonal Jacobi matrix operator. In this paper, we consider a generalisation of this relation with regard to connecting higher order Schrödinger-type operators with symmetric matrix operators with arbitrarily many nonzero diagonals above and below the main diagonal. We thus obtain spectral bounds for such matrices, similar in nature to the Lieb-Thirring inequalities.