On a Weyl-Titchmarsh Theory for Discrete Symplectic Systems on a Half Line

Author

Stephen L. Clark, Missouri University of Science and TechnologyFollow
Petr Zemánek

Editor(s)

Scott, Melvin

Abstract

Recently, Bohner and Sun [9] introduced basic elements of a Weyl–Titchmarsh theory into the study of discrete symplectic systems. We extend this development through the introduction of Weyl–Titchmarsh functions together with a preliminary study of their properties. A limit point criterion is described and characterized. Green’s function for the half-line is introduced as a limit of such functions in the regular case and half-line solutions obtained are seen to satisfy λ-dependent boundary conditions at infinity.

Recommended Citation

S. L. Clark and P. Zemánek, "On a Weyl-Titchmarsh Theory for Discrete Symplectic Systems on a Half Line," Applied Mathematics and Computation, Elsevier, Jan 2010.

The definitive version is available at https://doi.org/10.1016/j.amc.2010.08.029

Department(s)

Mathematics and Statistics

Keywords and Phrases

discrete symplectic system; Weyl-Titchmarsh M-function; regular spectral problem; singular spectral problem; Riccati equation; limit point case; limit circle case; Green's function

International Standard Serial Number (ISSN)

0096-3003

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2010 Elsevier, All rights reserved.

Publication Date

01 Jan 2010