# Commuting linear operators and algebraic decompositions

Archivum Mathematicum (2007)

- Volume: 043, Issue: 5, page 373-387
- ISSN: 0044-8753

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topGover, Rod A., and Šilhan, Josef. "Commuting linear operators and algebraic decompositions." Archivum Mathematicum 043.5 (2007): 373-387. <http://eudml.org/doc/250153>.

@article{Gover2007,

abstract = {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.},

author = {Gover, Rod A., Šilhan, Josef},

journal = {Archivum Mathematicum},

keywords = {commuting linear operators; decompositions; relative invertibility; commuting linear operators; decompositions; relative invertibility},

language = {eng},

number = {5},

pages = {373-387},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {Commuting linear operators and algebraic decompositions},

url = {http://eudml.org/doc/250153},

volume = {043},

year = {2007},

}

TY - JOUR

AU - Gover, Rod A.

AU - Šilhan, Josef

TI - Commuting linear operators and algebraic decompositions

JO - Archivum Mathematicum

PY - 2007

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 043

IS - 5

SP - 373

EP - 387

AB - 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.

LA - eng

KW - commuting linear operators; decompositions; relative invertibility; commuting linear operators; decompositions; relative invertibility

UR - http://eudml.org/doc/250153

ER -

## References

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