Gover, A. Rod; Šilhan, Josef Commuting linear operators and algebraic decompositions. (English) Zbl 1199.53020 Arch. Math., Brno 43, No. 5, 373-387 (2007). Summary: 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 \(P=P_0P_1\dots P_\ell \) 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. Cited in 2 Documents MSC: 53A30 Conformal differential geometry (MSC2010) 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) 53A55 Differential invariants (local theory), geometric objects Keywords:commuting linear operators; decompositions; relative invertibility × Cite Format Result Cite Review PDF Full Text: arXiv EuDML EMIS