About: Rayleigh principle for linear Hamiltonian systems without controllability

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In this paper we consider linear Hamiltonian differential systems without the controllability (or normality) assumption. We prove the Rayleigh principle for these systems with Dirichlet boundary conditions, which provides a variational characterization of the finite eigenvalues of the associated self-adjoint eigenvalue problem. This result generalizes the traditional Rayleigh principle to possibly abnormal linear Hamiltonian systems. The main tools are the extended Picone formula, which is proven here for this general setting, results on piecewise constant kernels for conjoined bases of the Hamiltonian system, and the oscillation theorem relating the number of proper focal points of conjoined bases with the number of finite eigenvalues. As applications we obtain the expansion theorem in the space of admissible functions without controllability and a result on coercivity of the corresponding quadratic functional. In this paper we consider linear Hamiltonian differential systems without the controllability (or normality) assumption. We prove the Rayleigh principle for these systems with Dirichlet boundary conditions, which provides a variational characterization of the finite eigenvalues of the associated self-adjoint eigenvalue problem. This result generalizes the traditional Rayleigh principle to possibly abnormal linear Hamiltonian systems. The main tools are the extended Picone formula, which is proven here for this general setting, results on piecewise constant kernels for conjoined bases of the Hamiltonian system, and the oscillation theorem relating the number of proper focal points of conjoined bases with the number of finite eigenvalues. As applications we obtain the expansion theorem in the space of admissible functions without controllability and a result on coercivity of the corresponding quadratic functional. (en)
Title	Rayleigh principle for linear Hamiltonian systems without controllability Rayleigh principle for linear Hamiltonian systems without controllability (en)
skos:prefLabel	Rayleigh principle for linear Hamiltonian systems without controllability Rayleigh principle for linear Hamiltonian systems without controllability (en)
skos:notation	RIV/00216224:14310/12:00057185!RIV13-GA0-14310___
http://linked.open...avai/predkladatel	Přírodovědecká fakulta
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GC201/09/J009), Z(MSM0021622409)
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Šimon Hilscher, Roman
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Masarykova univerzita / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	164163
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/12:00057185
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Linear Hamiltonian system; Rayleigh principle; Self-adjoint eigenvalue problem; Proper focal point; Conjoined basis; Finite eigenvalue; Oscillation theorem; Controllability; Normality; Quadratic functional (en)
http://linked.open.../riv/klicoveSlovo	Self-adjoint eigenvalue problem Controllability Conjoined basis Finite eigenvalue Linear Hamiltonian system Normality Oscillation theorem Proper focal point Quadratic functional Rayleigh principle
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[B68B3826B704]
http://linked.open...i/riv/nazevZdroje	ESAIM: Control, Optimisation and Calculus of Variations
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Oscillation and spectral theory of differential and difference systems
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	18
http://linked.open...iv/tvurceVysledku	Kratz, Werner Šimon Hilscher, Roman
http://linked.open...ain/vavai/riv/wos	000306431900010
http://linked.open...n/vavai/riv/zamer	Matematické struktury a jejich fyzikální aplikace
issn	1292-8119
number of pages	19 (xsd:int)
http://bibframe.org/vocab/doi	10.1051/cocv/2011104
http://localhost/t...ganizacniJednotka	14310
is http://linked.open...avai/riv/vysledek of	Rayleigh principle for linear Hamiltonian systems without controllability

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