On linear operators with an invariant subspace of functions

2004/01/05 by Yves Brihaye, Brihaye, Yves
Computer Science · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Physical sciences #Mathematical Physics (math-ph) #Polynomial and algebraic computation #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0401005

6 pages, LaTeX, discussion extended, reference added

openalex publication_date 2004/01/05 · arxiv created 2004/02/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let us denote \cal V, the finite dimensional vector spaces of functions of the form ψ(x) = p_n(x) + f(x) p_m(x) where p_n(x) and p_m(x) are arbitrary polynomials of degree at most n and m in the variable x while f(x) represents a fixed function of x. Conditions on m,n and f(x) are found such that families of linear differential operators exist which preserve \cal V. A special emphasis is accorded to the cases where the set of differential operators represents the envelopping algebra of some abstract algebra.

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