Holomorphic synthesis of monogenic functions of several quaternionic variables |
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Authors: | Victor P Palamodov |
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Institution: | (1) School of Mathematics, Tel Aviv University Ramat Aviv, 69978 Tel Aviv, Israel |
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Abstract: | The system of differential equations for polymonogenic functions of several quaternionic variables is an analogue of the
-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
-complex on Σ that provides a resolvennt for the sheaf of polymonogenic functions. |
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