Abstract and Applied Analysis

Weyl-Titchmarsh Theory for Hamiltonian Dynamic Systems

Shurong Sun, Martin Bohner, and Shaozhu Chen

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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.

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

First available in Project Euclid: 1 November 2010

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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

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