On the Non-commutative Neutrix Product of the Distributions $\delta ^{(r)}(x)$ and $x^{-s}\ln^m|x|$}
DOI:
https://doi.org/10.5644/SJM.02.2.08Keywords:
Distribution, delta-function, neutrix, neutrix limit, neutrix productAbstract
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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References
J.G. van der Corput, Introduction to the neutrix calculus, J. Anal. Math., 7 (1959-60), 291–398.
B. Fisher, The product of distributions, Quart. J. Math. Oxford, 22 (2) (1971), 291–298.
B. Fisher, A non-commutative neutrix product of distributions, Math. Nachr., 108 (1982), 117–127.
I.M. Gel’fand and G.E. Shilov, Generalized Functions, Vol. I, Academic Press, 1964.
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Published
12.06.2024
How to Cite
Fisher, B., Ege, I., & Özçag, E. (2024). On the Non-commutative Neutrix Product of the Distributions $\delta ^{(r)}(x)$ and $x^{-s}\ln^m|x|$}. Sarajevo Journal of Mathematics, 2(2), 211–221. https://doi.org/10.5644/SJM.02.2.08
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