On Linear Operators Preserving the Set of Positive Polynomials
نویسنده
چکیده
Following the classical approach of Pólya-Schur theory [14] we initiate in this paper the study of linear operators acting on R[x] and preserving either the set of positive univariate polynomials or similar sets of non-negative and elliptic polynomials.
منابع مشابه
Pde - Preserving Properties
A continuous linear operator T , on the space of entire functions in d variables, is PDE-preserving for a given set P ⊆ C[ξ1, ..., ξd] of polynomials if it maps every kernel-set ker P (D), P ∈ P, invariantly. It is clear that the set O(P) of PDE-preserving operators for P forms an algebra under composition. We study and link properties and structures on the operator side O(P) versus the corresp...
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