ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Comparative index and Sturmian theory for linear Hamiltonian systems. Journal of Differential Equations. San Diego, CA USA: ACADEMIC PRESS INC ELSEVIER SCIENCE, 2017, roč. 262, č. 2, s. 914-944. ISSN 0022-0396. Dostupné z: https://dx.doi.org/10.1016/j.jde.2016.09.043. |
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@article{1355407, author = {Šepitka, Peter and Šimon Hilscher, Roman}, article_location = {San Diego, CA USA}, article_number = {2}, doi = {http://dx.doi.org/10.1016/j.jde.2016.09.043}, keywords = {Linear Hamiltonian system; Sturmian separation theorem; Proper focal point; Comparative index; Conjoined basis; Nonoscillation; Controllability}, language = {eng}, issn = {0022-0396}, journal = {Journal of Differential Equations}, title = {Comparative index and Sturmian theory for linear Hamiltonian systems}, volume = {262}, year = {2017} }
TY - JOUR ID - 1355407 AU - Šepitka, Peter - Šimon Hilscher, Roman PY - 2017 TI - Comparative index and Sturmian theory for linear Hamiltonian systems JF - Journal of Differential Equations VL - 262 IS - 2 SP - 914-944 EP - 914-944 PB - ACADEMIC PRESS INC ELSEVIER SCIENCE SN - 00220396 KW - Linear Hamiltonian system KW - Sturmian separation theorem KW - Proper focal point KW - Comparative index KW - Conjoined basis KW - Nonoscillation KW - Controllability N2 - The comparative index was introduced by J. Elyseeva (2007) as an efficient tool in matrix analysis, which has fundamental applications in the discrete oscillation theory. In this paper we implement the comparative index into the theory of continuous time linear Hamiltonian systems, study its properties, and apply it to obtain new Sturmian separation theorems as well as new and optimal estimates for left and right proper focal points of conjoined bases of these systems on bounded intervals. We derive our results for general possibly abnormal (or uncontrollable) linear Hamiltonian systems. The results turn out to be new even in the case of completely controllable systems. We also provide several examples, which illustrate our new theory. ER -
ŠEPITKA, Peter a Roman ŠIMON HILSCHER. Comparative index and Sturmian theory for linear Hamiltonian systems. \textit{Journal of Differential Equations}. San Diego, CA USA: ACADEMIC PRESS INC ELSEVIER SCIENCE, 2017, roč.~262, č.~2, s.~914-944. ISSN~0022-0396. Dostupné z: https://dx.doi.org/10.1016/j.jde.2016.09.043.
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