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Quaternionic hyperfunctions on five-dimensional varieties in ℍ2

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Abstract

In this article we introduce a new notion of differential forms to describe the cohomology associated to the sheaf of regular functions in several quaternionic variables. We then use these differential forms to introduce and describe concretely a sheaf of quaternionic hyperfunctions as boundary values of regular functions in two quaternionic variables. We show how these ideas can be generalized to the case of monogenic functions in two vector variables with values in a Clifford algebra.

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Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Via Bonardi, 9, 20133, Milano, Italy

    Fabrizio Colombo, Alberto Damiano, Irene Sabadini & Daniele C. Struppa

  2. Mathematical Institute, Charles University, Sokolovska 83, Praha, Czech Republic

    Fabrizio Colombo, Alberto Damiano, Irene Sabadini & Daniele C. Struppa

  3. Department of Mathematics and Computer Science, Chapman University, 92866, Orange

    Fabrizio Colombo, Alberto Damiano, Irene Sabadini & Daniele C. Struppa

Authors
  1. Fabrizio Colombo
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  2. Alberto Damiano
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  3. Irene Sabadini
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  4. Daniele C. Struppa
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Correspondence to Fabrizio Colombo.

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Colombo, F., Damiano, A., Sabadini, I. et al. Quaternionic hyperfunctions on five-dimensional varieties in ℍ2. J Geom Anal 17, 435–454 (2007). https://doi.org/10.1007/BF02922091

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  • DOI: https://doi.org/10.1007/BF02922091

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