On a class of infinitely differentiable functions in ${\mathbb R}^n$ admitting holomorphic extension in ${\mathbb C}^n$

I. Kh. Musin; P. V. Yakovleva

On a class of infinitely differentiable functions in ${\mathbb R}^n$ admitting holomorphic extension in ${\mathbb C}^n$

Complex Variables 2017-12-15 v1

Authors: I. Kh. Musin , P. V. Yakovleva

Abstract

A space $G(M, \varPhi)$ of infinitely differentiable functions in ${\mathbb R}^n$ constructed with a help of a family $\varPhi=\{\varphi_m\}_{m=1}^{\infty}$ of real-valued functions $\varphi_m \in~C({\mathbb R}^n)$ 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 ${\mathbb C}^n$ . Imposed conditions on $M$ and $\varPhi$ allow to describe the space of such extensions.

Keywords

infinitely differentiable functions holomorphic extension entire functions logarithmically convex sequence clopen sets

Cite

@article{arxiv.1712.05125,
  title  = {On a class of infinitely differentiable functions in ${\mathbb R}^n$ admitting holomorphic extension in ${\mathbb C}^n$},
  author = {I. Kh. Musin and P. V. Yakovleva},
  journal= {arXiv preprint arXiv:1712.05125},
  year   = {2017}
}

On a class of infinitely differentiable functions in ${\mathbb R}^n$ admitting holomorphic extension in ${\mathbb C}^n$

Abstract

Keywords

Cite

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