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@article{916285,
author = {Šimon Hilscher, Roman and Zemánek, Petr},
article_location = {New York},
article_number = {738520},
doi = {http://dx.doi.org/10.1155/2011/738520},
keywords = {Time scale; Time scale symplectic system; Weyl-Titchmarsh theory; M(lambda)-function; Lagrange identity; Weyl disk; Weyl circle; Limit point case; Limit circle case; Linear Hamiltonian system; Discrete symplectic system; Eigenvalue problem},
language = {eng},
issn = {1085-3375},
journal = {Abstract and Applied Analysis},
title = {Weyl-Titchmarsh theory for time scale symplectic systems on half line},
url = {http://www.hindawi.com/journals/aaa/differential.difference.equations/},
volume = {2011},
year = {2011}
}
TY - JOUR
ID - 916285
AU - Šimon Hilscher, Roman - Zemánek, Petr
PY - 2011
TI - Weyl-Titchmarsh theory for time scale symplectic systems on half line
JF - Abstract and Applied Analysis
VL - 2011
IS - 738520
SP - 1-41
EP - 1-41
PB - Hindawi Publishing Corporation
SN - 10853375
KW - Time scale
KW - Time scale symplectic system
KW - Weyl-Titchmarsh theory
KW - M(lambda)-function
KW - Lagrange identity
KW - Weyl disk
KW - Weyl circle
KW - Limit point case
KW - Limit circle case
KW - Linear Hamiltonian system
KW - Discrete symplectic system
KW - Eigenvalue problem
UR - http://www.hindawi.com/journals/aaa/differential.difference.equations/
L2 - http://www.hindawi.com/journals/aaa/differential.difference.equations/
N2 - In this paper we develop the Weyl-Titchmarsh theory for time scale symplectic systems. We introduce the M(lambda)-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 in Applied Mathematics and Computation.
ER -
ŠIMON HILSCHER, Roman and Petr ZEMÁNEK. Weyl-Titchmarsh theory for time scale symplectic systems on half line. \textit{Abstract and Applied Analysis}. New York: Hindawi Publishing Corporation, 2011, vol.~2011, No~738520, p.~1-41. ISSN~1085-3375. Available from: https://dx.doi.org/10.1155/2011/738520.
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