We prove an Almansi Theorem for quaternionic polynomials %of the form $P(x)=sum_{k=0}^d x^ka_k$ and extend it to quaternionic slice-regular functions. We associate to every such function $f$, a pair $h_1$, $h_2$ of zonal harmonic functions such that $f=h_1-ar x h_2$. We apply this result to get mean value formulas and Poisson formulas for slice-regular quaternionic functions.

Almansi Theorem and Mean Value Formula for Quaternionic Slice-regular Functions / Perotti, Alessandro. - In: ADVANCES IN APPLIED CLIFFORD ALGEBRAS. - ISSN 0188-7009. - 30:(2020), pp. 6101-6111. [10.1007/s00006-020-01078-4]

Almansi Theorem and Mean Value Formula for Quaternionic Slice-regular Functions

Alessandro Perotti
2020

Abstract

We prove an Almansi Theorem for quaternionic polynomials %of the form $P(x)=sum_{k=0}^d x^ka_k$ and extend it to quaternionic slice-regular functions. We associate to every such function $f$, a pair $h_1$, $h_2$ of zonal harmonic functions such that $f=h_1-ar x h_2$. We apply this result to get mean value formulas and Poisson formulas for slice-regular quaternionic functions.
Perotti, Alessandro
Almansi Theorem and Mean Value Formula for Quaternionic Slice-regular Functions / Perotti, Alessandro. - In: ADVANCES IN APPLIED CLIFFORD ALGEBRAS. - ISSN 0188-7009. - 30:(2020), pp. 6101-6111. [10.1007/s00006-020-01078-4]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/270805
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