A generalized index theorem for monotone matrix-valued functions with applications to discrete oscillation theory

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F13%3A00065976" target="_blank" >RIV/00216224:14310/13:00065976 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1137/120873029" target="_blank" >http://dx.doi.org/10.1137/120873029</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/120873029" target="_blank" >10.1137/120873029</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A generalized index theorem for monotone matrix-valued functions with applications to discrete oscillation theory

Popis výsledku v původním jazyce

An index theorem is a tool for computing the change of the index (i.e., the number of negative eigenvalues) of a symmetric monotone matrix-valued function when its variable passes through a singularity. In 1995, the first author proved an index theorem in which a certain critical matrix coefficient is constant. In this paper, we generalize the above index theorem to the case when this critical matrix may be varying, but its rank, as well as the rank of some additional matrix, are constant. This includesas a special case the situation when this matrix has a constant image. We also show that the index theorem does not hold when the main assumption on constant ranks is violated. Our investigation is motivated by the oscillation theory of discrete symplectic systems with nonlinear dependence on the spectral parameter, which was recently developed by the second author and for which we obtain new oscillation theorems.

Název v anglickém jazyce

A generalized index theorem for monotone matrix-valued functions with applications to discrete oscillation theory

Popis výsledku anglicky

An index theorem is a tool for computing the change of the index (i.e., the number of negative eigenvalues) of a symmetric monotone matrix-valued function when its variable passes through a singularity. In 1995, the first author proved an index theorem in which a certain critical matrix coefficient is constant. In this paper, we generalize the above index theorem to the case when this critical matrix may be varying, but its rank, as well as the rank of some additional matrix, are constant. This includesas a special case the situation when this matrix has a constant image. We also show that the index theorem does not hold when the main assumption on constant ranks is violated. Our investigation is motivated by the oscillation theory of discrete symplectic systems with nonlinear dependence on the spectral parameter, which was recently developed by the second author and for which we obtain new oscillation theorems.

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

<a href="/cs/project/GAP201%2F10%2F1032" target="_blank" >GAP201/10/1032: Diferenční rovnice a dynamické rovnice na ,,time scales'' III</a><br>

Návaznosti

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

Rok uplatnění

2013

Kód důvěrnosti údajů

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

Název periodika

SIAM Journal on Matrix Analysis and Applications

ISSN

0895-4798

e-ISSN

—

Svazek periodika

34

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

16

Strana od-do

228-243

Kód UT WoS článku

000316855600011

EID výsledku v databázi Scopus

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