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= ℝ and T= ℤ 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.

Department(s)

Mathematics and Statistics

Sponsor(s)

China Postdoctoral Science Foundation Funded Project
University of Jinan (China). Fund of Doctoral Program Research
Natural Science Foundation of China
Natural Science Foundation of Shandong
Shandong Postdoctoral Foundation

Keywords and Phrases

Weyl-Titchmarsh Theory; Singular Linear Hamiltonian Dynamic Systems

Document Type

Article - Journal

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 2010 Hindawi Publishing Corporation, All rights reserved.

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