About: Multiplicities of focal points for discrete symplectic systems: revisited

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	In this note we define a notion of multiplicity of focal points for conjoined bases of discrete symplectic systems. We show that this definition is equivalent to the one given by Kratz in [Discrete oscillation, <i> J. Difference Equ. Appl. </i> <b> 9 </b> (2003), no. 1, 135--147] and, furthermore, it has a natural connection to the newly developed continuous time theory on linear Hamiltonian differential systems. Many results obtained recently by Bohner, Došlý, and Kratz regarding the nonnegativity of the corresponding discrete quadratic functionals, Sturmian separation and comparison theorems, and oscillation theorems relating the number of focal points of a certain special conjoined basis with the number of eigenvalues of the associated discrete symplectic eigenvalue problem, are now formulated in terms of this alternative definition of multiplicities. In this note we define a notion of multiplicity of focal points for conjoined bases of discrete symplectic systems. We show that this definition is equivalent to the one given by Kratz in [Discrete oscillation, <i> J. Difference Equ. Appl. </i> <b> 9 </b> (2003), no. 1, 135--147] and, furthermore, it has a natural connection to the newly developed continuous time theory on linear Hamiltonian differential systems. Many results obtained recently by Bohner, Došlý, and Kratz regarding the nonnegativity of the corresponding discrete quadratic functionals, Sturmian separation and comparison theorems, and oscillation theorems relating the number of focal points of a certain special conjoined basis with the number of eigenvalues of the associated discrete symplectic eigenvalue problem, are now formulated in terms of this alternative definition of multiplicities. (en)
Title	Multiplicities of focal points for discrete symplectic systems: revisited Multiplicities of focal points for discrete symplectic systems: revisited (en)
skos:prefLabel	Multiplicities of focal points for discrete symplectic systems: revisited Multiplicities of focal points for discrete symplectic systems: revisited (en)
skos:notation	RIV/00216224:14310/09:00028573!RIV11-GA0-14310___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/07/0145), P(KJB100190701), P(ME 891), Z(MSM0021622409)
http://linked.open...iv/cisloPeriodika	10
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Šimon Hilscher, Roman Zeidan, Vera Michel
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	328032
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/09:00028573
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Discrete symplectic system; Focal point; Multiplicity; Conjoined basis; Sturmian separation theorem; Sturmian comparison theorem; Moore-Penrose generalized inverse (en)
http://linked.open.../riv/klicoveSlovo	Sturmian comparison theorem Sturmian separation theorem Focal point Multiplicity Conjoined basis Discrete symplectic system Moore-Penrose generalized inverse
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[A06DB0292A8A]
http://linked.open...i/riv/nazevZdroje	Journal of Difference Equations and Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Difference equations and dynamic equations on time scales II Asymptotics, oscillation, and quadratic functionals in theory of dynamic equations http://linked.opendata.cz/resource/domain/vavai/projekt/ME%20891
http://linked.open...UplatneniVysledku	2009
http://linked.open...v/svazekPeriodika	15
http://linked.open...iv/tvurceVysledku	Zeidan, Vera Michel Šimon Hilscher, Roman
http://linked.open...ain/vavai/riv/wos	000278248300006
http://linked.open...n/vavai/riv/zamer	Matematické struktury a jejich fyzikální aplikace
issn	1023-6198
number of pages	10 (xsd:int)
http://localhost/t...ganizacniJednotka	14310
is http://linked.open...avai/riv/vysledek of	Multiplicities of focal points for discrete symplectic systems: revisited Multiplicities of focal points for discrete symplectic systems: revisited Multiplicities of focal points for discrete symplectic systems: revisited

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