"360483" . "Acta Applicandae Mathematicae" . . "000273785300012" . "P(LC505), S" . "RIV/00216224:14310/08:00035610" . "109" . . "Commuting Linear Operators and Decompositions; Applications to Einstein Manifolds"@en . "[798D9C32CDC7]" . "35"^^ . . . . . . . . . "14310" . "Commuting linear operators; Conformally invariant operators; Einstein manifolds; Symmetries of differential operators"@en . . . . "Commuting Linear Operators and Decompositions; Applications to Einstein Manifolds" . "2" . "2"^^ . . "Commuting Linear Operators and Decompositions; Applications to Einstein Manifolds" . "1"^^ . . "0167-8019" . "Gover, Rod" . "For linear operators which factor P=P0 P1 ... Pp , with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same questions for the factors, or certain compositions thereof. When the operators Pi are polynomial in other commuting operators D1,...,Dk then we show that, in a suitable sense, generically such factorisation of Pi yield decompositions algebraically. In the case of operators on a vector space over an algebraically closed field this boils down to elementary algebraic geometry arising from the polynomial formula for P. The results and formulae are independent of the Dj and so the theory provides a route to studying the solution space and the inhomogenous problem Pu=f without any attempt to 'diagonalise' the Dj."@en . . "\u0160ilhan, Josef" . "NL - Nizozemsko" . . "RIV/00216224:14310/08:00035610!RIV10-MSM-14310___" . "Commuting Linear Operators and Decompositions; Applications to Einstein Manifolds"@en . "For linear operators which factor P=P0 P1 ... Pp , with suitable assumptions concerning commutativity of the factors, we introduce several notions of a decomposition. When any of these hold then questions of null space and range are subordinated to the same questions for the factors, or certain compositions thereof. When the operators Pi are polynomial in other commuting operators D1,...,Dk then we show that, in a suitable sense, generically such factorisation of Pi yield decompositions algebraically. In the case of operators on a vector space over an algebraically closed field this boils down to elementary algebraic geometry arising from the polynomial formula for P. The results and formulae are independent of the Dj and so the theory provides a route to studying the solution space and the inhomogenous problem Pu=f without any attempt to 'diagonalise' the Dj." .