In this paper we present a new definition of regularity on the space O of Cayley numbers (often referred to as octonions), based on a Gateaux-like notion of derivative. We study the main properties of regular functions and , and we develop the basic elements of a function theory on O. Particular attention is given to the structure of the zero sets of such functions.
Regular functions on the space of Cayley numbers / Gentili, Graziano; Struppa, Daniele C.. - In: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS. - ISSN 0035-7596. - STAMPA. - 40 (1):(2010), pp. 225-241. [10.1216/RMJ-2010-40-1-225]
Regular functions on the space of Cayley numbers
GENTILI, GRAZIANO;
2010
Abstract
In this paper we present a new definition of regularity on the space O of Cayley numbers (often referred to as octonions), based on a Gateaux-like notion of derivative. We study the main properties of regular functions and , and we develop the basic elements of a function theory on O. Particular attention is given to the structure of the zero sets of such functions.
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