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Statements

Subject Item
n2:RIV%2F00216224%3A14310%2F07%3A00020419%21RIV10-MSM-14310___
rdf:type
n14:Vysledek skos:Concept
dcterms:description
In this paper we consider a bounded time scale T=[a,b], a quadratic functional F(x,u) defined over such time scale, and its perturbation G(x,u)=F(x,u)+\alpha|x(a)|^2, where the endpoints of F are zero, while the initial endpoint x(a) of G can vary and x(b) is zero. It is known that there is no restriction on x(a) in G when studying the positivity of these functionals. We prove that, when studying the nonnegativity, the initial state x(a) in G must be restricted to a certain subspace, which is the kernel of a specific conjoined basis of the associated time scale symplectic system. This result generalizes a known discrete-time special case, but it is new for the corresponding continuous-time case. We provide several examples which illustrate the theory. In this paper we consider a bounded time scale T=[a,b], a quadratic functional F(x,u) defined over such time scale, and its perturbation G(x,u)=F(x,u)+\alpha|x(a)|^2, where the endpoints of F are zero, while the initial endpoint x(a) of G can vary and x(b) is zero. It is known that there is no restriction on x(a) in G when studying the positivity of these functionals. We prove that, when studying the nonnegativity, the initial state x(a) in G must be restricted to a certain subspace, which is the kernel of a specific conjoined basis of the associated time scale symplectic system. This result generalizes a known discrete-time special case, but it is new for the corresponding continuous-time case. We provide several examples which illustrate the theory.
dcterms:title
Perturbation of nonnegative time scale quadratic functionals Perturbation of nonnegative time scale quadratic functionals
skos:prefLabel
Perturbation of nonnegative time scale quadratic functionals Perturbation of nonnegative time scale quadratic functionals
skos:notation
RIV/00216224:14310/07:00020419!RIV10-MSM-14310___
n3:aktivita
n16:P
n3:aktivity
P(1K04001), P(GA201/04/0580)
n3:dodaniDat
n12:2010
n3:domaciTvurceVysledku
n17:6860591 n17:3008312
n3:druhVysledku
n10:D
n3:duvernostUdaju
n19:S
n3:entitaPredkladatele
n21:predkladatel
n3:idSjednocenehoVysledku
441073
n3:idVysledku
RIV/00216224:14310/07:00020419
n3:jazykVysledku
n11:eng
n3:klicovaSlova
Quadratic functional; Nonnegativity; Positivity; Time scale; Time scale symplectic system; Hamiltonian system
n3:klicoveSlovo
n5:Time%20scale%20symplectic%20system n5:Nonnegativity n5:Time%20scale n5:Hamiltonian%20system n5:Quadratic%20functional n5:Positivity
n3:kontrolniKodProRIV
[16F5788B5597]
n3:mistoKonaniAkce
Mnichov
n3:mistoVydani
Londýn
n3:nazevZdroje
Difference Equations, Special Functions, and Orthogonal Polynomials
n3:obor
n13:BA
n3:pocetDomacichTvurcuVysledku
2
n3:pocetTvurcuVysledku
2
n3:projekt
n20:GA201%2F04%2F0580 n20:1K04001
n3:rokUplatneniVysledku
n12:2007
n3:tvurceVysledku
Růžičková, Viera Šimon Hilscher, Roman
n3:typAkce
n4:WRD
n3:wos
000261024200022
n3:zahajeniAkce
2005-01-01+01:00
s:numberOfPages
10
n15:hasPublisher
World Scientific
n18:isbn
978-981-270-643-0
n6:organizacniJednotka
14310