On regular harmonics of one quaternionic variable

Perotti, Alessandro (2005) On regular harmonics of one quaternionic variable. [Preprint]

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    We prove some results about the Fueter-regular homogeneous polynomials, which appear as components in the power series of any quaternionic regular function. Let B denote the unit ball in C2 ≅ H and S = δ B the group of unit quaternions. In §2.1 we obtain a differential condition that characterize the homogeneous polynomials whose restrictions to S extend as a regular polynomial. This result generalizes a similar characterization for holomorphic extensions of polynomials proved by Kytmanov. In §2.2 we show how to define an injective linear operator R: Hk(S)-> Uk Ψ between the space of complex-valued spherical harmonics and the H-module of regular homogeneous polynomials of degree k. In particular, we show how to construct bases of the module of regular homogeneous polynomials of a fixed degree starting from any choice of C-bases of the spaces of complex harmonic homogeneous polynomials.

    Item Type: Preprint
    Department or Research center: Mathematics
    Subjects: Q Science > QA Mathematics > QA299.6 Analysis
    Uncontrolled Keywords: Quaternionic regular functions, spherical harmonics
    Additional Information: Primary 32A30; Secondary 30G35, 32V10, 32W05
    Repository staff approval on: 27 Jul 2005

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