Boundedness of composition operator on several variable Paley-Wiener space

被引：0
|
作者：
Samanta, Amit [1 ]
Sarkar, Santanu [2 ]
机构：
[1] Ramakrishna Mission Vivekananda Educ & Res Inst, Dept Math, PO Belur Math, Howrah 711202, West Bengal, India
[2] Indian Inst Technol Ropar, Dept Math, Rupnagar 140001, Punjab, India
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2023年 / 660卷
关键词：
Composition operator; Paley-Wiener space; Reproducing kernel; Bessel?s function;
D O I：
10.1016/j.laa.2022.12.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we have considered composition operators on the several variable Paley-Wiener space L2 pi(Cn). We have proved that for any continuous function phi : Cn -> Cn the composition operator C phi on L2 pi(Cn) is bounded iff phi has the following form: phi(z) = Az + b, z is an element of Cn, where A is an element of GL(n,R) with ||A||op <= 1 and b is an element of Cn. Our proof is different from the single variable case and mainly depends on a theorem of Malgrange, some techniques from harmonic analysis and certain asymptotic behaviour of Bessel's function. (c) 2022 Elsevier Inc. All rights reserved.
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页码：66 / 79
页数：14
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