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.
S. Sun et al., "Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems," Abstract and Applied Analysis, Hindawi Publishing Corporation, Jan 2010.
The definitive version is available at https://doi.org/10.1155/2010/514760
Mathematics and Statistics
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
International Standard Serial Number (ISSN)
Article - Journal
© 2010 Hindawi Publishing Corporation, All rights reserved.
01 Jan 2010