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

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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.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Computer Science, University Goce Delcev, Stip, Republic of Macedonia

    M. Miteva & T. Atanasova-Pacemska

  2. Faculty of Electrical Engineering and Informational Technologies, Ss. Cyril and Methodius University, Skopje, Republic of Macedonia

    B. Jolevska-Tuneska

Authors
  1. M. Miteva
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  2. B. Jolevska-Tuneska
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  3. T. Atanasova-Pacemska
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Correspondence to M. Miteva.

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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 52, No. 1, pp. 13–25, 2018

Original Russian Text Copyright © by M. Miteva, B. Jolevska-Tuneska, and T. Atanasova-Pacemska

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Miteva, M., Jolevska-Tuneska, B. & Atanasova-Pacemska, T. Results on the Colombeau Products of the Distribution x −r−1/2+ with the Distributions x −k−1/2− and x k−1/2− . Funct Anal Its Appl 52, 9–20 (2018). https://doi.org/10.1007/s10688-018-0202-y

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  • DOI: https://doi.org/10.1007/s10688-018-0202-y

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