Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 341, Issue 1, Pages 649-659Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2007.10.030
Keywords
internal sets; Colombeau generalized functions
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This paper is devoted to the study of generalized functions as pointwise functions (so-called internal functions) on certain sets of generalized points (so-called internal sets). We treat the case of the Colombeau algebras of generalized functions, for which these notions have turned out to constitute a fundamental technical tool. We provide general foundations for the notion of internal functions and internal sets and prove a saturation principle. Various applications to Colombeau algebras are given. (C) 2007 Elsevier Inc. All rights reserved.
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