Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 421, Issue 1, Pages 415-435Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2014.07.014
Keywords
Colombeau algebra; Nonlinear generalized function; Smoothing kernel; Smoothing operator; Basic space; Sheaf property
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Funding
- Austrian Science Fund (FWF) [P23714]
- Austrian Science Fund (FWF) [P 23714] Funding Source: researchfish
- Austrian Science Fund (FWF) [P23714] Funding Source: Austrian Science Fund (FWF)
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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.
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