Publication result detail

Riccati inequality and other results for discrete symplectic systems.

HILSCHER, R.; RŮŽIČKOVÁ, V.

Original Title

Riccati inequality and other results for discrete symplectic systems.

English Title

Riccati inequality and other results for discrete symplectic systems.

Type

WoS Article

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.

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

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

Key words in English

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

Authors

HILSCHER, R.; RŮŽIČKOVÁ, V.

Released

31.08.2006

ISBN

0022-247X

Periodical

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Volume

322

Number

2

State

United States of America

Pages from

1083

Pages to

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 APPLICATIONS",
  year="2006",
  volume="322",
  number="2",
  pages="1083--1098",
  issn="0022-247X"
}