On the Non-commutative Neutrix Product of the Distributions $\delta ^{(r)}(x)$ and $x^{-s}\ln^m|x

It is proved that the non-commutative neutrix product of the distributions $ \delta ^{(r)}(x)$ and $x^{-s} \ln^m|x|$ exists and $$ \delta ^{(r)}(x) \circ x^{-s} \ln^m |x| = 0 $$ for $r,m=0,1,2, \ldots$ and $s = 1,2, \ldots.$   2000 Mathematics Subject Classification. 46F10

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Bibliographic Details
Published inSarajevo journal of mathematics Vol. 2; no. 2; pp. 211 - 221
Main Authors Fisher, Brian, Ege, Inci, Özçag, Emin
Format Journal Article
LanguageEnglish
Published 12.06.2024
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Summary:It is proved that the non-commutative neutrix product of the distributions $ \delta ^{(r)}(x)$ and $x^{-s} \ln^m|x|$ exists and $$ \delta ^{(r)}(x) \circ x^{-s} \ln^m |x| = 0 $$ for $r,m=0,1,2, \ldots$ and $s = 1,2, \ldots.$   2000 Mathematics Subject Classification. 46F10
ISSN:1840-0655
2233-1964
DOI:10.5644/SJM.02.2.08