Composition operators on the Schwartz space

被引：11

作者：

Galbis, Antonio ^{[1
]}

Jorda, Enrique ^{[2
]}

机构：

[1] Univ Valencia, Dept Anal Matemat, E-46100 Burjassot, Valencia, Spain

[2] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Campus Alcoi,Plaza Ferrandiz & Carbonell S-N, Alcoy 03801, Alicante, Spain

来源：

REVISTA MATEMATICA IBEROAMERICANA | 2018年 / 34卷 / 01期

关键词：

Composition operator; composite function problem; space of rapidly decreasing functions; DIMENSIONAL SMOOTH SYMBOLS; CLOSED RANGE; DIFFERENTIABLE FUNCTIONS; SUBANALYTIC SETS;

D O I：

10.4171/RMI/989

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study composition operators on the Schwartz space of rapidly decreasing functions. We prove that such a composition operator is never a compact operator and we obtain necessary or sufficient conditions for the range of the composition operator to be closed. These conditions are expressed in terms of multipliers for the Schwartz class and the closed range property of the corresponding operator considered in the space of smooth functions.

引用

页码：397 / 412

页数：16

共 18 条

[1]

[Anonymous], 1961, Uspekhi Mat. Nauk

[2]

[Anonymous], 1972, Ergebnisse der Mathematik und ihrer Grenzgebiete

[3] Composite differentiable functions [J].