Publication detail

Perturbation of nonnegative time scale quadratic functionals

HILSCHER, R. RŮŽIČKOVÁ, V.

Original Title

Perturbation of nonnegative time scale quadratic functionals

Type

conference paper

Language

English

Original Abstract

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.

Keywords

Quadratic functional, Nonnegativity, Positivity, Time scale, Time scale symplectic system, Hamiltonian system

Authors

HILSCHER, R.; RŮŽIČKOVÁ, V.

Released

1. 5. 2007

ISBN

978-981-270-643-0

Book

DIFFERENCE EQUATIONS, SPECIAL FUNCTIONS AND ORTHOGONAL POLYNOMIALS Proceedings of the International Conference

Pages from

266

Pages to

275

Pages count

10

BibTex

@inproceedings{BUT20211,
  author="Roman Šimon {Hilscher} and Viera {Štoudková Růžičková}",
  title="Perturbation of nonnegative time scale quadratic functionals",
  booktitle="DIFFERENCE EQUATIONS, SPECIAL FUNCTIONS AND ORTHOGONAL POLYNOMIALS Proceedings of the International Conference",
  year="2007",
  pages="266--275",
  isbn="978-981-270-643-0"
}