Podrobný výpis o publikaci

Using the machinery of unitary spherical harmonics due to Koornwinder, Folland and other authors, we obtain expansions for the Szegö and the weighted Bergman kernels of M-harmonic functions, i.e. functions annihilated by the invariant Laplacian on the unit ball of the complex n-space. This yields, among others, an explicit formula for the M-harmonic Szegö kernel in terms of multivariable as well as single-variable hypergeometric functions, and also shows that most likely there is no explicit (“closed”) formula for the corresponding weighted Bergman kernels.