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

Facets (new session)
Description
Metadata
Settings
- owl:sameAs
- Inference Rule:

About: A generalized index theorem for monotone matrix-valued functions with applications to discrete oscillation theory Goto Sponge NotDistinct Permalink

An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	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 includes as 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. 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 includes as 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. (en)
Title	A generalized index theorem for monotone matrix-valued functions with applications to discrete oscillation theory A generalized index theorem for monotone matrix-valued functions with applications to discrete oscillation theory (en)
skos:prefLabel	A generalized index theorem for monotone matrix-valued functions with applications to discrete oscillation theory A generalized index theorem for monotone matrix-valued functions with applications to discrete oscillation theory (en)
skos:notation	RIV/00216224:14310/13:00065976!RIV14-GA0-14310___
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GAP201/10/1032)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Šimon Hilscher, Roman
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Masarykova univerzita / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	58634
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/13:00065976
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Index theorem; Rank theorem; Limit theorem; Oscillation theorem; Discrete symplectic system; Sturm--Liouville difference equation (en)
http://linked.open.../riv/klicoveSlovo	Index theorem Limit theorem Rank theorem Sturm--Liouville difference equation Discrete symplectic system Oscillation theorem
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[382C6057A234]
http://linked.open...i/riv/nazevZdroje	SIAM Journal on Matrix Analysis and Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Difference equations and dynamic equations on time scales III
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	34
http://linked.open...iv/tvurceVysledku	Kratz, Werner Šimon Hilscher, Roman
http://linked.open...ain/vavai/riv/wos	000316855600011
issn	0895-4798
number of pages	16 (xsd:int)
http://bibframe.org/vocab/doi	10.1137/120873029
http://localhost/t...ganizacniJednotka	14310

Faceted Search & Find service v1.16.118 as of Jun 21 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Jun 21 2024, on Linux (x86_64-pc-linux-gnu), Single-Server Edition (126 GB total memory, 48 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software