Commuting Linear Operators and Decompositions; Applications to Einstein Manifolds

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F08%3A00035610" target="_blank" >RIV/00216224:14310/08:00035610 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Commuting Linear Operators and Decompositions; Applications to Einstein Manifolds

Popis výsledku v původním jazyce

For linear operators which factor P=P0 P1 ... Pp , with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same questions for the factors, or certain compositions thereof. When the operators Pi are polynomial in other commuting operators D1,...,Dk then we show that, in a suitable sense, generically such factorisation of Pi yield decompositions algebraically. In the case of operators on a vector space over an algebraically closed field this boils down to elementary algebraic geometry arising from the polynomial formula for P. The results and formulae are independent of the Dj and so the theory provides a routeto studying the solution space and the inhomogenous problem Pu=f without any attempt to 'diagonalise' the Dj.

Název v anglickém jazyce

Commuting Linear Operators and Decompositions; Applications to Einstein Manifolds

Popis výsledku anglicky

For linear operators which factor P=P0 P1 ... Pp , with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same questions for the factors, or certain compositions thereof. When the operators Pi are polynomial in other commuting operators D1,...,Dk then we show that, in a suitable sense, generically such factorisation of Pi yield decompositions algebraically. In the case of operators on a vector space over an algebraically closed field this boils down to elementary algebraic geometry arising from the polynomial formula for P. The results and formulae are independent of the Dj and so the theory provides a routeto studying the solution space and the inhomogenous problem Pu=f without any attempt to 'diagonalise' the Dj.

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/LC505" target="_blank" >LC505: Centrum Eduarda Čecha pro algebru a geometrii</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2008

Kód důvěrnosti údajů

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

Název periodika

Acta Applicandae Mathematicae

ISSN

0167-8019

e-ISSN

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Svazek periodika

109

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

35

Strana od-do

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Kód UT WoS článku

000273785300012

EID výsledku v databázi Scopus

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