Division algebras of slice functions
Copyright policy )Division algebras of slice functions
AbstractThis 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.
- University of Florence Italy
- University of Trento Italy
- New York University Italy
Mathematics - Complex Variables, functions of one hypercomplex variable, geometric function theory, functions of one hypercomplex variable; division algebras; octonions, Nonassociative division algebras, Functions of hypercomplex variables and generalized variables, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination, FOS: Mathematics, meromorphic functions, 30G35 (Primary) 17A35, 30C15, 30C80, 30D30 (Secondary), Complex Variables (math.CV), Mathematics - Complex Variables; Mathematics - Complex Variables; 30G35 (Primary) 17A35, 30C15, 30C80, 30D30 (Secondary), Meromorphic functions of one complex variable (general theory), division algebras
Mathematics - Complex Variables, functions of one hypercomplex variable, geometric function theory, functions of one hypercomplex variable; division algebras; octonions, Nonassociative division algebras, Functions of hypercomplex variables and generalized variables, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), Maximum principle, Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination, FOS: Mathematics, meromorphic functions, 30G35 (Primary) 17A35, 30C15, 30C80, 30D30 (Secondary), Complex Variables (math.CV), Mathematics - Complex Variables; Mathematics - Complex Variables; 30G35 (Primary) 17A35, 30C15, 30C80, 30D30 (Secondary), Meromorphic functions of one complex variable (general theory), division algebras
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