Topology and functoriality in (C, E, P)-algebras. Application to singular differential problems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:359

Article

Delcroix, Antoine

关键词: Regularization of data;    Regularization of problems;    Distributions;    Nonlinear generalized functions;    Nonlinear problems;    Sharp topology;    Wave equation;   

DOI  :  10.1016/j.jmaa.2009.05.046

来源: Elsevier

【 摘 要 】

We show that a new definition of the asymptotic structure of the (C, E, P)-algebras (which are a refinement of the Colombeau Generalized Algebras) allows to define a natural topology on them. Furthermore, this topology can be mixed with functorial aspects of the construction in order to give extension principles, which give powerful tools to solve singular differential problems in this framework. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free