About: Commuting linear operators and algebraic decompositions

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	For commuting linear operators $P_0,P_1,\dots ,P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1\cdots P_\ell$ in terms of the component operators or combinations thereof. In particular the general inhomogeneous problem $Pu=f$ reduces to a system of simpler problems. These problems capture the structure of the solution and range spaces and, if the operators involved are differential, then this gives an effective way of lowering the differential order of the problem to be studied. Suitable systems of operators may be treated analogously. For a class of decompositions the higher symmetries of a composition $P$ may be derived from generalised symmmetries of the component operators $P_i$ in the system. For commuting linear operators $P_0,P_1,\dots ,P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1\cdots P_\ell$ in terms of the component operators or combinations thereof. In particular the general inhomogeneous problem $Pu=f$ reduces to a system of simpler problems. These problems capture the structure of the solution and range spaces and, if the operators involved are differential, then this gives an effective way of lowering the differential order of the problem to be studied. Suitable systems of operators may be treated analogously. For a class of decompositions the higher symmetries of a composition $P$ may be derived from generalised symmmetries of the component operators $P_i$ in the system. (en)
Title	Commuting linear operators and algebraic decompositions Commuting linear operators and algebraic decompositions (en)
skos:prefLabel	Commuting linear operators and algebraic decompositions Commuting linear operators and algebraic decompositions (en)
skos:notation	RIV/00216224:14310/07:00023987!RIV10-MSM-14310___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(LC505), Z(MSM 143100009)
http://linked.open...iv/cisloPeriodika	5
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	414211
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/07:00023987
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Commuting linear operators; decompositions; relative invertibility (en)
http://linked.open.../riv/klicoveSlovo	decompositions relative invertibility Commuting linear operators
http://linked.open...odStatuVydavatele	CZ - Česká republika
http://linked.open...ontrolniKodProRIV	[94ED88E1CCB2]
http://linked.open...i/riv/nazevZdroje	Archivum Mathematicum
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	2007
http://linked.open...v/svazekPeriodika	43
http://linked.open...iv/tvurceVysledku	Gover, Rod Šilhan, Josef
http://linked.open...n/vavai/riv/zamer	http://linked.opendata.cz/resource/domain/vavai/zamer/MSM%20143100009
issn	1212-5059
number of pages	14 (xsd:int)
http://localhost/t...ganizacniJednotka	14310

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