On Hypercyclic Operators in Weighted Spaces of Infinitely Differentiable Functions

被引：0

作者：

Rakhimova, A. I. ^{[1
]}

机构：

[1] Bashkir State Univ, Ufa 450074, Russia

来源：

MATHEMATICAL NOTES | 2023年 / 114卷 / 1-2期

关键词：

infinitely differentiable functions; hypercyclic operator; convolution operator;

D O I：

10.1134/S0001434623070258

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A differentiation-invariant weighted Frechet space E(phi) of infinitely differentiable functions in R-n generated by a countable family phi of continuous real-valued functions in R-n is considered. It is shown that, under minimal restrictions on phi, any continuous linear operator on E(phi) that is not a scalar multiple of the identity mapping and commutes with the partial differentiation operators is hypercyclic. Examples of hypercyclic operators in E(phi) are presented for cases in which the space E(phi) is translation invariant.

引用

页码：242 / 249

页数：8

共 8 条

[1] UNIVERSAL VECTORS FOR OPERATORS ON SPACES OF HOLOMORPHIC-FUNCTIONS [J].