The functional analytic foundation of Colombeau algebras

被引：8
|
作者：
Nigsch, E. A. [1 ]
机构：
[1] Univ Vienna, Fak Math, A-1090 Vienna, Austria
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 421卷 / 01期
基金：
奥地利科学基金会;
关键词：
Colombeau algebra; Nonlinear generalized function; Smoothing kernel; Smoothing operator; Basic space; Sheaf property; GLOBAL THEORY; DISTRIBUTIONS;
D O I：
10.1016/j.jmaa.2014.07.014
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Colombeau algebras constitute a convenient framework for performing nonlinear operations like multiplication on Schwartz distributions. Many variants and modifications of these algebras exist for various applications. We present a functional analytic approach placing these algebras in a unifying hierarchy, which clarifies their structural properties as well as their relation to each other. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码：415 / 435
页数：21
相关论文
共 50 条
12345