Titlebook: Regular Functions of a Quaternionic Variable; Graziano Gentili,Caterina Stoppato,Daniele C. Stru Book 2022Latest edition The Editor(s) (if

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Infinite Products,The aim of this chapter is proving the Weierstrass Factorization Theorem for quaternionic entire functions. To do so, we introduce several tools: we consider infinite (pointwise and) regular products and we study their convergence, using the principal branch of the quaternionic logarithm.

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Integral Representations,Regular quaternionic functions inherit a version of the Cauchy Theorem from the holomorphic complex functions. Let us begin with some notations.

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Maximum Modulus Theorem and Applications,The complex Maximum Modulus Principle has a perfect analog for regular functions, proven with the aid of the Splitting Lemma ..

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Generalizations,After the introduction of the notion of (slice) regular quaternionic function, the same approach was adopted over the algebra of octonions . in [.] and the Clifford algebra . in [.].

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Function Theory Over Non-symmetric Slice Domains,This chapter turns back to the study of regular functions . initiated in Sect. .. While Chaps. .–. focused on the case when Ω is a symmetric slice domain, we now consider slice domains in general (dropping the symmetry hypothesis).

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