Structure theorems for linear and non-linear differential operators admitting invariant polynomial subspaces
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 t...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2007 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/51451 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/51451 |
| Access Level: | acceso abierto |
| Palabra clave: | 51-73 Diffusion-equations Calogero Algebras Spaces Física-Modelos matemáticos Física matemática |
| Sumario: | 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. |
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