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2011 Weyl-Titchmarsh Theory for Time Scale Symplectic Systems on Half Line
Roman Šimon Hilscher, Petr Zemánek
Abstr. Appl. Anal. 2011(SI1): 1-41 (2011). DOI: 10.1155/2011/738520


We develop the Weyl-Titchmarsh theory for time scale symplectic systems. We introduce the M(λ) -function, study its properties, construct the corresponding Weyl disk and Weyl circle, and establish their geometric structure including the formulas for their center and matrix radii. Similar properties are then derived for the limiting Weyl disk. We discuss the notions of the system being in the limit point or limit circle case and prove several characterizations of the system in the limit point case and one condition for the limit circle case. We also define the Green function for the associated nonhomogeneous system and use its properties for deriving further results for the original system in the limit point or limit circle case. Our work directly generalizes the corresponding discrete time theory obtained recently by S. Clark and P. Zemánek (2010). It also unifies the results in many other papers on the Weyl-Titchmarsh theory for linear Hamiltonian differential, difference, and dynamic systems when the spectral parameter appears in the second equation. Some of our results are new even in the case of the second-order Sturm-Liouville equations on time scales.


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Roman Šimon Hilscher. Petr Zemánek. "Weyl-Titchmarsh Theory for Time Scale Symplectic Systems on Half Line." Abstr. Appl. Anal. 2011 (SI1) 1 - 41, 2011.


Published: 2011
First available in Project Euclid: 12 August 2011

zbMATH: 1217.34144
MathSciNet: MR2773642
Digital Object Identifier: 10.1155/2011/738520

Rights: Copyright © 2011 Hindawi


Vol.2011 • No. SI1 • 2011
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