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Holomorphic synthesis of monogenic functions of several quaternionic variables

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Abstract

The system of differential equations for polymonogenic functions of several quaternionic variables is an analogue of the\(\bar \partial \)-equation in complex analysis. We give a representation of polymonogenic functions by means of integration of a family of σ-holomorphic functions as σ runs over the variety Σ of all complex structures ℍ ≅ ℂ2 which are consistent with the metric and an orientation in ℍ. The variety Σ is isomorphic to the manifold of all proper right ideals in the complexified quaternionic algebra and has a natural complex analytic structure. We construct a\(\tilde \partial \)-complex on Σ that provides a resolvennt for the sheaf of polymonogenic functions.

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  1. School of Mathematics, Tel Aviv University Ramat Aviv, 69978, Tel Aviv, Israel

    Victor P. Palamodov

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  1. Victor P. Palamodov
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Palamodov, V.P. Holomorphic synthesis of monogenic functions of several quaternionic variables. J. Anal. Math. 78, 177–204 (1999). https://doi.org/10.1007/BF02791133

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  • DOI: https://doi.org/10.1007/BF02791133

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