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Title: On the composition of the distributions x-s+ lnmx+ and xμ+
Authors: Fisher, Brian
First Published: 2009
Publisher: University of Belgrade and Academic Mind
Citation: Applicable Analysis and Discrete Mathematics 2009 Volume 3, Issue 2, Pages: 212-223
Abstract: Let F be a distribution and let f be a locally summable function. The distribution F(f) is defined as the neutrix limit of the sequence {Fn(f)}, where Fn(x) = F(x)*δn(x) and {δn(x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function δ(x). The composition of the distributions x-s + lnm x+ and xμ + is proved to exist and be equal to μmx-sμ + lnm x+ for μ > 0 and s,m = 1, 2,....
DOI Link: 10.2298/AADM0902212F
ISSN: 1452-8630
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Made available with explicit permission from the publisher.
Description: 2000 Mathematics Subject Classification. 46F10
Appears in Collections:Published Articles, Dept. of Mathematics

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