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 $k$.
|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|
Available Versions of this Item
- On regular harmonics of one quaternionic variable. (deposited 27 Jul 2005)
- On regular harmonics of one quaternionic variable. (deposited 29 Nov 2005)[Currently Displayed]
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