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Statements

Subject Item
n2:RIV%2F00216224%3A14310%2F08%3A00035610%21RIV10-MSM-14310___
rdf:type
skos:Concept n15:Vysledek
dcterms:description
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 route to studying the solution space and the inhomogenous problem Pu=f without any attempt to 'diagonalise' the Dj. 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 route to studying the solution space and the inhomogenous problem Pu=f without any attempt to 'diagonalise' the Dj.
dcterms:title
Commuting Linear Operators and Decompositions; Applications to Einstein Manifolds Commuting Linear Operators and Decompositions; Applications to Einstein Manifolds
skos:prefLabel
Commuting Linear Operators and Decompositions; Applications to Einstein Manifolds Commuting Linear Operators and Decompositions; Applications to Einstein Manifolds
skos:notation
RIV/00216224:14310/08:00035610!RIV10-MSM-14310___
n3:aktivita
n12:S n12:P
n3:aktivity
P(LC505), S
n3:cisloPeriodika
2
n3:dodaniDat
n10:2010
n3:domaciTvurceVysledku
n18:6901816
n3:druhVysledku
n8:J
n3:duvernostUdaju
n16:S
n3:entitaPredkladatele
n4:predkladatel
n3:idSjednocenehoVysledku
360483
n3:idVysledku
RIV/00216224:14310/08:00035610
n3:jazykVysledku
n9:eng
n3:klicovaSlova
Commuting linear operators; Conformally invariant operators; Einstein manifolds; Symmetries of differential operators
n3:klicoveSlovo
n5:Einstein%20manifolds n5:Conformally%20invariant%20operators n5:Commuting%20linear%20operators n5:Symmetries%20of%20differential%20operators
n3:kodStatuVydavatele
NL - Nizozemsko
n3:kontrolniKodProRIV
[798D9C32CDC7]
n3:nazevZdroje
Acta Applicandae Mathematicae
n3:obor
n14:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n11:LC505
n3:rokUplatneniVysledku
n10:2008
n3:svazekPeriodika
109
n3:tvurceVysledku
Gover, Rod Šilhan, Josef
n3:wos
000273785300012
s:issn
0167-8019
s:numberOfPages
35
n13:organizacniJednotka
14310