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A differential criterium for regularity of quaternionic functions

✍ Scribed by Alessandro Perotti

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 87 KB
Volume: 337
Category: Article
ISSN: 1631-073X
DOI: 10.1016/s1631-073x(03)00284-x

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✦ Synopsis

Let Ω ⊆ C 2 . We prove that there exist differential operators T and N, with complex coefficients, such that a function f : Ω → H of class C 1 is regular if and only if (N -jT )f = 0 on ∂Ω (j a basic quaternion) and f is harmonic on Ω. At the same time we generalize a result of Kytmanov and Aizenberg. We show that a complex harmonic function h on Ω (∂Ω connected) is holomorphic if and only if ∂n h = aL(h) on ∂Ω, where ∂n is the normal part of ∂, L is a tangential Cauchy-Riemann operator and a ∈ C.

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