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2007 On the Noncommutative Neutrix Product of Distributions
Emin Özçaḡ, İnci Ege, Haşmet Gürçay, Biljana Jolevska-Tuneska
Abstr. Appl. Anal. 2007: 1-10 (2007). DOI: 10.1155/2007/81907

Abstract

Let f and g be distributions and let g n = ( g * δ n ) ( x ) , where δ n ( x ) is a certain sequence converging to the Dirac-delta function δ ( x ) . The noncommutative neutrix product f g of f and g is defined to be the neutrix limit of the sequence { f g n } , provided the limit h exists in the sense that N‐ lim n f ( x ) g n ( x ) , φ ( x ) = h ( x ) , φ ( x ) , for all test functions in 𝒟 . In this paper, using the concept of the neutrix limit due to van der Corput (1960), the noncommutative neutrix products x + r ln x + x r 1 ln x and x r 1 ln x x + r ln x + are proved to exist and are evaluated for r = 1 , 2 , . It is consequently seen that these two products are in fact equal.

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Emin Özçaḡ. İnci Ege. Haşmet Gürçay. Biljana Jolevska-Tuneska. "On the Noncommutative Neutrix Product of Distributions." Abstr. Appl. Anal. 2007 1 - 10, 2007. https://doi.org/10.1155/2007/81907

Information

Published: 2007
First available in Project Euclid: 27 February 2008

zbMATH: 1165.46018
MathSciNet: MR2365812
Digital Object Identifier: 10.1155/2007/81907

Rights: Copyright © 2007 Hindawi

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