Abstract and Applied Analysis

Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems

Shurong Sun, Martin Bohner, and Shaozhu Chen

Full-text: Open access

Abstract

We establish the Weyl-Titchmarsh theory for singular linear Hamiltonian dynamic systems on a time scale 𝕋 , which allows one to treat both continuous and discrete linear Hamiltonian systems as special cases for 𝕋 = and 𝕋 = within one theory and to explain the discrepancies between these two theories. This paper extends the Weyl-Titchmarsh theory and provides a foundation for studying spectral theory of Hamiltonian dynamic systems. These investigations are part of a larger program which includes the following: (i) M ( λ ) theory for singular Hamiltonian systems, (ii) on the spectrum of Hamiltonian systems, (iii) on boundary value problems for Hamiltonian dynamic systems.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 514760, 18 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620712

Digital Object Identifier
doi:10.1155/2010/514760

Mathematical Reviews number (MathSciNet)
MR2607129

Zentralblatt MATH identifier
1187.37090

Citation

Sun, Shurong; Bohner, Martin; Chen, Shaozhu. Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems. Abstr. Appl. Anal. 2010 (2010), Article ID 514760, 18 pages. doi:10.1155/2010/514760. https://projecteuclid.org/euclid.aaa/1288620712


Export citation