On regular harmonics of one quaternionic variable

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

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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. We obtain a differential condition that characterizes the homogeneous polynomials whose trace on the unit sphere extends as a regular polynomial. We apply this result to define an injective linear operator from the space of complex spherical harmonics to the module of regular homogeneous polynomials of a fixed degree $k$.

    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: 29 Nov 2005

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