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Commuting linear operators and algebraic decompositions

Rod A. Gover;  Josef Šilhan — 2007

Archivum Mathematicum

For commuting linear operators P 0 , P 1 , ⋯ , P ℓ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition P = P 0 P 1 ⋯ P ℓ in terms of the component operators or combinations thereof. In particular the general inhomogeneous problem P u = 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...

Aspects of parabolic invariant theory

Gover, Rod A. — 1999

Proceedings of the 18th Winter School "Geometry and Physics"

A certain family of homogeneous spaces is investigated. Basic invariant operators for each of these structures are presented and some analogies to Levi-Civita connections of Riemannian geometry are pointed out.

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