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Statements

Subject Item
n2:RIV%2F00216224%3A14310%2F07%3A00023987%21RIV10-MSM-14310___
rdf:type
skos:Concept n19:Vysledek
dcterms: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.
dcterms:title
Commuting linear operators and algebraic decompositions Commuting linear operators and algebraic decompositions
skos:prefLabel
Commuting linear operators and algebraic decompositions Commuting linear operators and algebraic decompositions
skos:notation
RIV/00216224:14310/07:00023987!RIV10-MSM-14310___
n3:aktivita
n6:Z n6:P
n3:aktivity
P(LC505), Z(MSM 143100009)
n3:cisloPeriodika
5
n3:dodaniDat
n12:2010
n3:domaciTvurceVysledku
n16:6901816
n3:druhVysledku
n10:J
n3:duvernostUdaju
n8:S
n3:entitaPredkladatele
n18:predkladatel
n3:idSjednocenehoVysledku
414211
n3:idVysledku
RIV/00216224:14310/07:00023987
n3:jazykVysledku
n14:eng
n3:klicovaSlova
Commuting linear operators; decompositions; relative invertibility
n3:klicoveSlovo
n13:Commuting%20linear%20operators n13:relative%20invertibility n13:decompositions
n3:kodStatuVydavatele
CZ - Česká republika
n3:kontrolniKodProRIV
[94ED88E1CCB2]
n3:nazevZdroje
Archivum Mathematicum
n3:obor
n17:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n15:LC505
n3:rokUplatneniVysledku
n12:2007
n3:svazekPeriodika
43
n3:tvurceVysledku
Šilhan, Josef Gover, Rod
n3:zamer
n9:MSM%20143100009
s:issn
1212-5059
s:numberOfPages
14
n4:organizacniJednotka
14310