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
  • [1] The category of Colombeau algebras
    Lorenzo Luperi Baglini
    Paolo Giordano
    Monatshefte für Mathematik, 2017, 182 : 649 - 674
  • [2] The category of Colombeau algebras
    Luperi Baglini, Lorenzo
    Giordano, Paolo
    MONATSHEFTE FUR MATHEMATIK, 2017, 182 (03): : 649 - 674
  • [3] New versions of the Colombeau algebras
    Shelkovich, VM
    MATHEMATISCHE NACHRICHTEN, 2005, 278 (11) : 1318 - 1340
  • [4] FULL AND SPECIAL COLOMBEAU ALGEBRAS
    Grosser, M.
    Nigsch, E. A.
    PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2018, 61 (04) : 961 - 994
  • [5] Colombeau algebras without asymptotics
    Nigsch, Eduard A.
    JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, 2019, 10 (01) : 133 - 154
  • [6] Colombeau algebras without asymptotics
    Eduard A. Nigsch
    Journal of Pseudo-Differential Operators and Applications, 2019, 10 : 133 - 154
  • [7] NATURAL TOPOLOGIES ON COLOMBEAU ALGEBRAS
    Aragona, Jorge
    Fernandez, Roseli
    Juriaans, Stanley O.
    TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2009, 34 (01) : 161 - 180
  • [8] Unifying order structures for Colombeau algebras
    Giordano, Paolo
    Nigsch, Eduard A.
    MATHEMATISCHE NACHRICHTEN, 2015, 288 (11-12) : 1286 - 1302
  • [9] Notes on regularity results in Colombeau algebras
    Oberguggenberger, M.
    INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2006, 17 (2-3) : 101 - 107
  • [10] An overall view of stochastics in Colombeau related algebras
    Çapar, U
    Aktuglu, H
    STOCHASTIC ANALYSIS AND RELATED TOPICS VIII, 2003, 53 : 67 - 90
12345