RT Journal Article
T1 Structure theorems for linear and non-linear differential operators admitting invariant polynomial subspaces
A1 Gómez-Ullate Otaiza, David
A1 Kamran, Niky
A1 Milson, Robert
AB In this paper we derive structure theorems which characterize the spaces of linear and non-linear differential operators that preserve finite dimensional subspaces generated by polynomials in one or several variables. By means of the useful concept of deficiency, we can write an explicit basis for these spaces of differential operators. In the case of linear operators, these results apply to the theory of quasi-exact solvability in quantum mechanics, especially in the multivariate case where the Lie algebraic approach is harder to apply. In the case of non-linear operators, the structure theorems in this paper can be applied to the method of finding special solutions of non-linear evolution equations by nonlinear separation of variables.
PB American Institute of Mathematical Sciences
SN 1078-0947
YR 2007
FD 2007-05
LK https://hdl.handle.net/20.500.14352/51451
UL https://hdl.handle.net/20.500.14352/51451
LA eng
NO © American Institute of Mathematical Sciences.
DS Docta Complutense
RD 25 abr 2025