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@article{1212340, author = {Šimon Hilscher, Roman and Zemánek, Petr}, article_location = {London}, article_number = {3}, doi = {http://dx.doi.org/10.1080/10236198.2014.997227}, keywords = {Symplectic system; time scale; Weyl disk; square integrable solution; limit point case; limit circle case; linear Hamiltonian system; limit circle invariance}, language = {eng}, issn = {1023-6198}, journal = {Journal of Difference Equations and Applications}, title = {Time scale symplectic systems with analytic dependence on spectral parameter}, volume = {21}, year = {2015} }
TY - JOUR ID - 1212340 AU - Šimon Hilscher, Roman - Zemánek, Petr PY - 2015 TI - Time scale symplectic systems with analytic dependence on spectral parameter JF - Journal of Difference Equations and Applications VL - 21 IS - 3 SP - 209-239 EP - 209-239 PB - Taylor and Francis SN - 10236198 KW - Symplectic system KW - time scale KW - Weyl disk KW - square integrable solution KW - limit point case KW - limit circle case KW - linear Hamiltonian system KW - limit circle invariance N2 - This paper is devoted to the study of time scale symplectic systems with polynomial and analytic dependence on the complex spectral parameter lambda. We derive fundamental properties of these systems (including the Lagrange identity) and discuss their connection with systems known in the literature, in particular with linear Hamiltonian systems. In analogy with the linear dependence on lambda, we present a construction of the Weyl disks and determine the number of linearly independent square integrable solutions. These results extend the discrete time theory considered recently by the authors. To our knowledge, in the continuous time case this concept is new. We also establish the invariance of the limit circle case for a special quadratic dependence on lambda and its extension to two (generally nonsymplectic) time scale systems, which yields new results also in the discrete case. The theory is illustrated by several examples. ER -
ŠIMON HILSCHER, Roman a Petr ZEMÁNEK. Time scale symplectic systems with analytic dependence on spectral parameter. \textit{Journal of Difference Equations and Applications}. London: Taylor and Francis, roč.~21, č.~3, s.~209-239. ISSN~1023-6198. doi:10.1080/10236198.2014.997227. 2015.
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