Endomorphisms of the space of higher-order entire functions and infinite-order differential operators

被引：2

作者：

Ishimura, Ryuichi ^{[1
]}

机构：

[1] Chiba Univ, Fac Sci, Dept Math & Informat, Chiba 2638522, Japan

来源：

KYUSHU JOURNAL OF MATHEMATICS | 2007年 / 61卷 / 01期

关键词：

entire functions in several variables; partial differential operator of infinite order;

D O I：

10.2206/kyushujm.61.83

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the space of entire functions for a given proximate order and a semi-norm, and show that a continuous endomorphism of this space is represented naturally as a partial differential operator of infinite order with entire function coefficients. Then, in the case of higher order, we study the relationship between the continuous endomorphisms and the linear partial differential operators of infinite order by means of the growth of the symbol of the operators.

引用

页码：83 / 94

页数：12