The basic results of a new theory of regular functions of a quaternionic variable have been recently stated, following an idea of Cullen. In this paper we prove the minimum modulus principle and the open mapping theorem for regular functions. The proofs involve some peculiar geometric properties of such functions which are of independent interest.
The open mapping theorem for regular quaternionic functions / Gentili, Graziano; Stoppato, Caterina. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 0391-173X. - STAMPA. - VIII(4):(2009), pp. 805-815. [10.2422/2036-2145.2009.4.07]
The open mapping theorem for regular quaternionic functions
GENTILI, GRAZIANO;STOPPATO, CATERINA
2009
Abstract
The basic results of a new theory of regular functions of a quaternionic variable have been recently stated, following an idea of Cullen. In this paper we prove the minimum modulus principle and the open mapping theorem for regular functions. The proofs involve some peculiar geometric properties of such functions which are of independent interest.
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