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Some remarks on zeroes of monogenic functions

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Abstract

There are not so many deep results about zero points of monogenic functions, due to the fact that there are too many things that can happen: zeroes are not isolated, zero sets are not disjoint (e.g. zero curves may cross each other). However, the Jacobian matrix of the monogenic function controls how large the zero sets will be, at least if its rank is constant; for example, if the Jacobian is an invertible matrix in a zero point of a monogenic function, then this point is anisolated zero.

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  1. Institute of Applied Mathematics I, TU Freiberg, Germany

    Thomas Hempfling

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  1. Thomas Hempfling
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Hempfling, T. Some remarks on zeroes of monogenic functions. AACA 11 (Suppl 2), 107–115 (2001). https://doi.org/10.1007/BF03219126

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