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Functional Analysis and Its Applications

, Volume 52, Issue 1, pp 9–20 | Cite as

Results on the Colombeau Products of the Distribution x + r−1/2 with the Distributions x k−1/2 and x k−1/2

  • M. Miteva
  • B. Jolevska-Tuneska
  • T. Atanasova-Pacemska
Article

Abstract

Results on the products of the distribution x + r−1/2 with the distributions x k−1/2 and x k−1/2 are obtained in the differential algebra G(ℝ) of Colombeau generalized functions, which contains the space D′(ℝ) of Schwartz distributions as a subspace; in this algebra the notion of association is defined, which is a faithful generalization of weak equality in G(ℝ). This enables treating the results in terms of distributions again.

Key words

distribution Colombeau algebra Colombeau generalized functions multiplication of distributions 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • M. Miteva
    • 1
  • B. Jolevska-Tuneska
    • 2
  • T. Atanasova-Pacemska
    • 1
  1. 1.Department of Mathematics, Faculty of Computer ScienceUniversity Goce DelcevStipRepublic of Macedonia
  2. 2.Faculty of Electrical Engineering and Informational TechnologiesSs. Cyril and Methodius UniversitySkopjeRepublic of Macedonia

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