Limit circle invariance for two differential systems on time scales

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F15%3A00080585" target="_blank" >RIV/00216224:14310/15:00080585 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1002/mana.201400005" target="_blank" >http://dx.doi.org/10.1002/mana.201400005</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/mana.201400005" target="_blank" >10.1002/mana.201400005</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Limit circle invariance for two differential systems on time scales

Popis výsledku v původním jazyce

In this paper we consider two linear differential systems on a time scale. Both systems depend linearly on a complex spectral parameter lambda. We prove that if all solutions of these two systems are square integrable with respect to a given weight matrix for one value lambda, then this property is preserved for all complex values lambda. This result extends and improves the corresponding continuous time statement, which was derived by Walker (1975) for two non-hermitian linear Hamiltonian systems, to appropriate differential systems on arbitrary time scales. The result is new even in the purely discrete case, or in the scalar time scale case, as well as when both time scale systems coincide. The latter case also generalizes a limit circle invariance criterion for symplectic systems on time scales, which was recently derived by the authors.

Název v anglickém jazyce

Limit circle invariance for two differential systems on time scales

Popis výsledku anglicky

In this paper we consider two linear differential systems on a time scale. Both systems depend linearly on a complex spectral parameter lambda. We prove that if all solutions of these two systems are square integrable with respect to a given weight matrix for one value lambda, then this property is preserved for all complex values lambda. This result extends and improves the corresponding continuous time statement, which was derived by Walker (1975) for two non-hermitian linear Hamiltonian systems, to appropriate differential systems on arbitrary time scales. The result is new even in the purely discrete case, or in the scalar time scale case, as well as when both time scale systems coincide. The latter case also generalizes a limit circle invariance criterion for symplectic systems on time scales, which was recently derived by the authors.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

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

Rok uplatnění

2015

Kód důvěrnosti údajů

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

Název periodika

Mathematische Nachrichten

ISSN

0025-584X

e-ISSN

—

Svazek periodika

288

Číslo periodika v rámci svazku

5-6

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

14

Strana od-do

696-709

Kód UT WoS článku

000353034400017

EID výsledku v databázi Scopus

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