This work studies slice functions over finite-dimensional division algebras. Their zero sets are studied in detail along with their multiplicative inverses, for which some unexpected phenomena are discovered. The results are applied to prove some useful properties of the subclass of slice regular functions, previously known only over quaternions. Firstly, they are applied to derive from the maximum modulus principle a version of the minimum modulus principle, which is in turn applied to prove the open mapping theorem. Secondly, they are applied to prove, in the context of the classification of singularities, the counterpart of the Casorati-Weierstrass theorem.

Division algebras of slice functions / Ghiloni, Riccardo; Perotti, Alessandro; Stoppato, Caterina. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS. - ISSN 0308-2105. - ELETTRONICO. - 150:4(2019), pp. 2055-2082. [10.1017/prm.2019.13]

Division algebras of slice functions

Riccardo Ghiloni;Alessandro Perotti;
2019

Abstract

This work studies slice functions over finite-dimensional division algebras. Their zero sets are studied in detail along with their multiplicative inverses, for which some unexpected phenomena are discovered. The results are applied to prove some useful properties of the subclass of slice regular functions, previously known only over quaternions. Firstly, they are applied to derive from the maximum modulus principle a version of the minimum modulus principle, which is in turn applied to prove the open mapping theorem. Secondly, they are applied to prove, in the context of the classification of singularities, the counterpart of the Casorati-Weierstrass theorem.
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Ghiloni, Riccardo; Perotti, Alessandro; Stoppato, Caterina
Division algebras of slice functions / Ghiloni, Riccardo; Perotti, Alessandro; Stoppato, Caterina. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS. - ISSN 0308-2105. - ELETTRONICO. - 150:4(2019), pp. 2055-2082. [10.1017/prm.2019.13]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/190627
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