About: Commuting Linear Operators and Decompositions; Applications to Einstein Manifolds

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
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. (en)
Title	Commuting Linear Operators and Decompositions; Applications to Einstein Manifolds Commuting Linear Operators and Decompositions; Applications to Einstein Manifolds (en)
skos:prefLabel	Commuting Linear Operators and Decompositions; Applications to Einstein Manifolds Commuting Linear Operators and Decompositions; Applications to Einstein Manifolds (en)
skos:notation	RIV/00216224:14310/08:00035610!RIV10-MSM-14310___
http://linked.open...avai/riv/aktivita	P S
http://linked.open...avai/riv/aktivity	P(LC505), S
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Šilhan, Josef
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	360483
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/08:00035610
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Commuting linear operators; Conformally invariant operators; Einstein manifolds; Symmetries of differential operators (en)
http://linked.open.../riv/klicoveSlovo	Commuting linear operators Einstein manifolds Symmetries of differential operators Conformally invariant operators
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[798D9C32CDC7]
http://linked.open...i/riv/nazevZdroje	Acta Applicandae Mathematicae
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	Eduard Čech Center for Algebra and Geometry
http://linked.open...UplatneniVysledku	2008
http://linked.open...v/svazekPeriodika	109
http://linked.open...iv/tvurceVysledku	Gover, Rod Šilhan, Josef
http://linked.open...ain/vavai/riv/wos	000273785300012
issn	0167-8019
number of pages	35 (xsd:int)
http://localhost/t...ganizacniJednotka	14310

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