1998/12/18 by Yuri Kozitsky, Kozitsky, Yuri, Lech Wołowski +2
Mathematics · #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Meromorphic and Entire Functions #math.CV #math.FA
paper · pdf · doi:10.48550/arxiv.math/9812111
31 pages, LaTeX, submitted to Journal d'Analyse Mathematique
arxiv created 1998/12/18 · openalex publication_date 1998/12/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A scale of the Frechet spaces of exponential type entire functions of one complex variable is considered. Certain special properties of subsets of these spaces consisting of Laguerre entire functions, which are obtained as uniform limits on compact subsets of the complex plane of polynomials with real nonpositive zeros only, are described. A class of infinite order differential operators which act between these Frechet spaces is inrtoduced and studied. In particular, it is shown that this class preserves the set of Laguerre entire functions. The results obtained are then used to obtain and to study the solutions of a certain initial value problem.