Note on the Distribution Composition \((x_+^\mu )^\lambda \)

Abstract

The composition of the distributions \(x^\lambda \) and \(x_+^\mu \) is evaluated for \(\lambda = -1,-2,\ldots \quad \mu >0\) and \(\lambda \mu \in {{\mathbb {Z}}}^- .\) Further results are deduced.

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Acknowledgments

The second author was supported by Tubitak. This work was supported by the research project “Functional spaces, topological and statistical aspects and their application in electrical engineering” financed by State University “Goce Delcev”—Stip, Republic of Macedonia.

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Correspondence to Biljana Jolevska-Tuneska.

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The authors declare that they have no conflict of interest.

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Communicated by See Keong Lee.

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Lazarova, L., Jolevska-Tuneska, B., Aktürk, İ. et al. Note on the Distribution Composition \((x_+^\mu )^\lambda \) . Bull. Malays. Math. Sci. Soc. 41, 709–721 (2018). https://doi.org/10.1007/s40840-016-0342-2

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Keywords

  • Distribution
  • Composition of distributions
  • Neutrix calculus
  • Neutrix limit
  • Neutrix composition
  • Hadamard’s finite part

Mathematics Subject Classification

  • Primary 46F10
  • Secondary 46F30