Titlebook: Regular Functions of a Quaternionic Variable; Graziano Gentili,Caterina Stoppato,Daniele C. Stru Book 20131st edition Springer-Verlag Berl

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Regular Functions of a Quaternionic Variable978-3-642-33871-7Series ISSN 1439-7382 Series E-ISSN 2196-9922

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https://doi.org/10.1007/978-3-642-33871-730G35, 30B10, 30C15, 30E20, 30C80; Schwarz‘s lemma; functions of hypercomplex variables and generalize

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Definitions and Basic Results,Let . be a domain in the space of quaternions ., namely, an open connected subset of . and let . denote the 2-sphere of quaternionic imaginary units. We define the notion of regular function as follows.

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Infinite Products,We consider an infinite product of quaternions . and, for ., we denote by . the partial products. In analogy with the complex case (see [4]), we give the following definition.

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Singularities,In this section we construct the ring of quotients of regular functions. We begin by presenting the definition of regular reciprocal of ., which involves the operations of regular conjugation and symmetrization presented in ..