On linear operators with an invariant subspace of functions
نویسنده
چکیده
Let us denote V, the finite dimensional vector spaces of functions of the form ψ(x) = pn(x)+ f(x)pm(x) where pn(x) and pm(x) are arbitrary polynomials of degree at most n andm in the variable x while f(x) represents a fixed function of x. Conditions onm,n and f(x) are found such that families of linear differential operators exist which preserve V. A special emphasis is accorded to the cases where the set of differential operators represents the envelopping algebra of some abstract algebra. ∗[email protected]
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