Publication detail

Riccati inequality and other results for discrete symplectic systems.

HILSCHER, R. RŮŽIČKOVÁ, V.

Czech title

Riccatiho nerovnost a další výsledky pro diskrétní symplektické systémy

English title

Riccati inequality and other results for discrete symplectic systems.

Type

journal article in Web of Science

Language

en

Original abstract

In this paper we establish several new results regarding the positivity and nonnegativity of discrete quadratic functionals F associated with discrete symplectic systems. In particular, we derive (i) the Riccati inequality for the positivity of F with separated endpoints, (ii) a characterization of the nonnegativity of F for the case of general (jointly varying) endpoints, and (iii) several perturbation-type inequalities regarding the nonnegativity of F with zero endpoints. Some of these results are new even for the special case of discrete Hamiltonian systems.

Czech abstract

V tomto článku uvádíme několik nových výsledků týkajících se pozitivity a nezápornosti diskrétních kvadratických funkcionálů F přidružených k diskrétním symplektickým systémům. Zejména odvodíme (i) Riccatiho nerovnost pro pozitivitu F se separovanými konci, (ii) charakterizaci nezápornosti F s obecnými konci a (iii) několik nerovností pro perturbované funkcionály a nezápornost F s nulovými konci. Některé tyto výsledky jsou nové i pro speciální případ diskrétních Hamiltonovských systémů.

English abstract

In this paper we establish several new results regarding the positivity and nonnegativity of discrete quadratic functionals F associated with discrete symplectic systems. In particular, we derive (i) the Riccati inequality for the positivity of F with separated endpoints, (ii) a characterization of the nonnegativity of F for the case of general (jointly varying) endpoints, and (iii) several perturbation-type inequalities regarding the nonnegativity of F with zero endpoints. Some of these results are new even for the special case of discrete Hamiltonian systems.

Keywords in English

Discrete symplectic system; Quadratic functional; Nonnegativity; Positivity; Riccati inequality; Riccati equation; Conjoined basis; Sturmian theorem

Released

31.08.2006

ISSN

0022-247X

Journal

Journal of Mathematical Analysis and Application

Volume

322

Number

2

Pages from–to

1083–1098

Pages count

15

BIBTEX


@article{BUT43690,
  author="Roman Šimon {Hilscher} and Viera {Štoudková Růžičková},
  title="Riccati inequality and other results for discrete symplectic systems.",
  journal="Journal of Mathematical Analysis and Application",
  year="2006",
  volume="322",
  number="2",
  month="August",
  pages="1083--1098",
  issn="0022-247X"
}