Positivity of quadratic functionals on time scales: necessity

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F01%3A00008163" target="_blank" >RIV/00216224:14310/01:00008163 - isvavai.cz</a>

Result on the web

—

DOI - Digital Object Identifier

—

Result language

angličtina

Original language name

Positivity of quadratic functionals on time scales: necessity

Original language description

In this work we establish that disconjugacy of a linear Hamiltonian system on time scales is a necessary condition for the positivity of the corresponding quadratic functional. We employ a certain minimal normality (controllability) assumption. Hence, the open problems stated by the author in [15], [16] are solved with the result that positivity of the quadratic functional is equivalent with disconjugacy of the Hamiltonian system on the interval under consideration. The general approach on time scales Tinvolves, as special cases, the well known continuous case for T=R and recently developed discrete one for T=Z, so that they are unified. As applications, Sturmian type separation and comparison theorems on time scales are also provided.

Czech name

Positivity of quadratic functionals on time scales: necessity

Czech description

In this work we establish that disconjugacy of a linear Hamiltonian system on time scales is a necessary condition for the positivity of the corresponding quadratic functional. We employ a certain minimal normality (controllability) assumption. Hence, the open problems stated by the author in [15], [16] are solved with the result that positivity of the quadratic functional is equivalent with disconjugacy of the Hamiltonian system on the interval under consideration. The general approach on time scales Tinvolves, as special cases, the well known continuous case for T=R and recently developed discrete one for T=Z, so that they are unified. As applications, Sturmian type separation and comparison theorems on time scales are also provided.

Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

—

Project

<a href="/en/project/GA201%2F98%2F0677" target="_blank" >GA201/98/0677: Difference equations and their applications</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2001

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Mathematische Nachrichten

ISSN

0025-584X

e-ISSN

—

Volume of the periodical

226

Issue of the periodical within the volume

1

Country of publishing house

DE - GERMANY

Number of pages

14

Pages from-to

85-98

UT code for WoS article

—

EID of the result in the Scopus database

—