A remark on projective limits of function spaces

2017/04/19 by Aggeliki Kampoukou, Kampoukou, Aggeliki, Vassili Nestoridis +1
Mathematics · #30H #32C18 #46A13 #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1704.05780

openalex publication_date 2017/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Omega subset of C^d be an open set and Km, m = 1, 2, . . . an exhaustion of Omega by compact subsets of Omega. We set Omega_m = int(Km) and let Xm(Omega_m) be a topological space of holomorphic functions on Omega_m between A^ infinity (Omega_m) and H(Omega_m). Then we show that the projective limit of the family Xm(Omega_m), m = 1, 2, . . . , under the restriction maps is homeomorphic and linearly isomorphic to the Frechet space H(Omega), idependently of the choice of the spaces Xm(Omega_m).

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