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  • In this paper we provide a survey of characterizations of the nonnegativity and positivity of quadratic functionals arising in the theory of linear Hamiltonian and symplectic systems. We study these functionals on traditional continuous time domain (under and without controllability), on discrete domain, and on time scale domain which unifies and extends both previous types. For each case we distinguish functionals with zero, separated, and jointly varying endpoints. The presented conditions are formulated in terms of the properties of a special conjoined basis of the considered linear system. It is now easy to compare all the results - between continuous, discrete, and time scale cases, between the zero, separated, and jointly varying endpoits, and between the nonnegativity and positivity.
  • In this paper we provide a survey of characterizations of the nonnegativity and positivity of quadratic functionals arising in the theory of linear Hamiltonian and symplectic systems. We study these functionals on traditional continuous time domain (under and without controllability), on discrete domain, and on time scale domain which unifies and extends both previous types. For each case we distinguish functionals with zero, separated, and jointly varying endpoints. The presented conditions are formulated in terms of the properties of a special conjoined basis of the considered linear system. It is now easy to compare all the results - between continuous, discrete, and time scale cases, between the zero, separated, and jointly varying endpoits, and between the nonnegativity and positivity. (en)
Title
  • Definiteness of quadratic functionals for Hamiltonian and symplectic systems: A survey
  • Definiteness of quadratic functionals for Hamiltonian and symplectic systems: A survey (en)
skos:prefLabel
  • Definiteness of quadratic functionals for Hamiltonian and symplectic systems: A survey
  • Definiteness of quadratic functionals for Hamiltonian and symplectic systems: A survey (en)
skos:notation
  • RIV/00216224:14310/09:00028574!RIV10-MSM-14310___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/07/0145), P(KJB100190701), P(ME 891), Z(MSM0021622409)
http://linked.open...iv/cisloPeriodika
  • 1
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 309263
http://linked.open...ai/riv/idVysledku
  • RIV/00216224:14310/09:00028574
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • Linear Hamiltonian system; Discrete symplectic system; Time scale; Time scale symplectic system; Quadratic functional; Conjoined basis; Focal point; Nonnegativity; Positivity (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • IN - Indická republika
http://linked.open...ontrolniKodProRIV
  • [E854237B8DCC]
http://linked.open...i/riv/nazevZdroje
  • International Journal of Difference Equations
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 4
http://linked.open...iv/tvurceVysledku
  • Zemánek, Petr
  • Šimon Hilscher, Roman
http://linked.open...n/vavai/riv/zamer
issn
  • 0973-6069
number of pages
http://localhost/t...ganizacniJednotka
  • 14310
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