On a class of infinitely differentiable functions in \mathbb Rⁿ admitting holomorphic extension in \mathbb Cⁿ

2017/12/14 by I. Kh. Musin, Musin, I. Kh., P. V. Yakovleva +1
Mathematics · #32A15 #46E10 #Advanced Banach Space Theory #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Approximation and Integration #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1712.05125

openalex publication_date 2017/12/14 · openalex created_date 2017/12/22 · openalex updated_date 2026/07/28

Abstract

A space G(M, \varPhi) of infinitely differentiable functions in \mathbb Rⁿ constructed with a help of a family \varPhi=\φ_m\_m=1^∞ of real-valued functions φ_m ∈~C(\mathbb Rⁿ) and a logarithmically convex sequence M of positive numbers is considered in the article. In view of conditions on M each function of G(M, \varPhi) can be extended to an entire function in \mathbb Cⁿ. Imposed conditions on M and \varPhi allow to describe the space of such extensions.

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