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Weyl-Titchmarsh Theory for Time Scale Symplectic Systems on Half Line
Joint Authors
Simon Hilscher, Roman
Zemánek, Petr
Source
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-41, 41 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-03-09
Country of Publication
Egypt
No. of Pages
41
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Simon Hilscher, Roman& Zemánek, Petr. 2011. Weyl-Titchmarsh Theory for Time Scale Symplectic Systems on Half Line. Abstract and Applied Analysis،Vol. 2011, no. 2011, pp.1-41.
https://search.emarefa.net/detail/BIM-494781
Modern Language Association (MLA)
Simon Hilscher, Roman& Zemánek, Petr. Weyl-Titchmarsh Theory for Time Scale Symplectic Systems on Half Line. Abstract and Applied Analysis No. 2011 (2011), pp.1-41.
https://search.emarefa.net/detail/BIM-494781
American Medical Association (AMA)
Simon Hilscher, Roman& Zemánek, Petr. Weyl-Titchmarsh Theory for Time Scale Symplectic Systems on Half Line. Abstract and Applied Analysis. 2011. Vol. 2011, no. 2011, pp.1-41.
https://search.emarefa.net/detail/BIM-494781
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-494781