Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON THE COMMUTATIVE PRODUCT OF DISTRIBUTIONS

  • Fisher Bring (Department of Mathematics University of Leicester) ;
  • Tas Kenan (Department of Mathematics and Computer Science Faculty of Arts and Science Cankaya University)
  • Published : 2006.03.01
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Abstract

The commutative products of the distributions $x^r\;ln^p\;{\mid}x{\mid}\;and\;x^{-r-1}ln^q\;{\mid}x{\mid}$ and of sgn x $x^r\;ln^p\;{\mid}x{\mid}\;and\;sgn\;x\;x^{-r-1}ln^q\;{\mid}x{\mid}$ are evaluated for $r=0,\;\pm1,\;\pm2,...\;and\;p,\;q=0,1,2,....$

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References

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  3. B. Fishe, The product of the distributions $x_+^{-r-\frac{1}{2}}$ and $x_-^{-r-\frac{1}{2}$, Proc. Cambridge Philos. Soc. 71 (1971), 123-130
  4. B. Fishe, The product of the distributions $x^{-r}$ and $\mu^{(r-1)}$(x), Proc. Cambridge Philos. Soc. 72 (1972), 201-204
  5. B. Fishe, Some results on the product of distributions, Proc. Cambridge Philos. Soc. 73 (1973), 317-325
  6. I. M. Gel'fand and G. E. Shilov, Generalized Functions, Vol. I, Academic Press, 1964
  7. L. Schwartz, Theorie des Distributions, Tome I, Actualites Sci. Ind., no. 1091, Hermann & Cie., Paris 1950, 148

Cited by

  1. Several results on the commutative neutrix product of distributions vol.18, pp.8, 2007, https://doi.org/10.1080/10652460701366169