arXiv subjects

Agata Bezubik

Publications and source records attributed to Agata Bezubik.

2 recordsLinked to original sources

arXiv2011

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

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..

math.CA↗

arXiv2006

A New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of SO(d)-Finite Functions

This paper presents recent results obtained by the authors (partly in collaboration with A. Dabrowska) concerning expansions of zonal functions on Euclidean spheres into spherical harmonics and some applications of such expansions for problems involving Fourier transforms of functions with rotational symmetry. The method used to derive the expansion formula is based entirely on differential methods and completely avoids the use of various integral identities commonly used in this context. Some new identities for the Fourier transform are derived and as a byproduct seemingly new recurrence relations for the classical Bessel functions are obtained.

math-ph↗