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On the singular Bochner-Martinelli integral

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Abstract

The Bochner-Martinelli (B.-M.) kernel inherits, forn≥2, only some of properties of the Cauchy kernel in ℂ. For instance it is known that the singular B.-M. operatorM n is not an involution forn≥2. M. Shapiro and N. Vasilevski found a formula forM 22 using methods of quaternionic analysis which are essentially complex-twodimensional. The aim of this article is to present a formula forM 2n for anyn≥2. We use now Clifford Analysis but forn=2 our formula coincides, of course, with the above-mentioned one.

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Authors and Affiliations

  1. Departamento de Matemáticas, ESFM-IPN, Mexico City, MEXICO

    R. Rocha-Chávez & M. Shapiro

  2. N.F.W.O., BELGIUM

    F. Sommen (Senior Research Associate)

Authors
  1. R. Rocha-Chávez
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  2. M. Shapiro
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  3. F. Sommen
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Rocha-Chávez, R., Shapiro, M. & Sommen, F. On the singular Bochner-Martinelli integral. Integr equ oper theory 32, 354–365 (1998). https://doi.org/10.1007/BF01203775

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  • DOI: https://doi.org/10.1007/BF01203775

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