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arXiv · 1112.0648

On spherical expansions of smooth $\gr{SU}{n}$-zonal functions on the unit sphere in $\NC^n$

Agata Bezubik·Aleksander Strasburger
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Abstract

We give a self-contained presentation of a novel approach to a construction of spherical harmonic expansions on the unit sphere in $\NC^n$. We derive a new formula for coefficients of the expansion of a smooth zonal function defined on the unit sphere and apply it in some special cases. The expansion for the Poisson--Szegö kernel for the unit ball in $\NC^n$ obtained by our method coincides with the result obtained originally by G. Folland, and on the other hand disproves results recently presented in a paper of V.A. Menegatto et al..

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Agata Bezubik, Aleksander Strasburger. 2011-12-03. On spherical expansions of smooth $\gr{SU}{n}$-zonal functions on the unit sphere in $\NC^n$. https://arxiv.org/abs/1112.0648

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