论文标题
M谐波繁殖球上的核
M-harmonic reproducing kernels on the ball
论文作者
论文摘要
使用Koornwinder，Folland和其他作者引起的统一球形谐波的机械，我们〜获得Szegö的扩展以及$ M $ harmonic函数的加权伯格曼核，即不变的laplacian在$ n $ n $ -space的单位球上不变的laplacian an灭的功能。在多变量和单个可验证的超几何功能方面，这产生了$ M $ harmonicszegöKernel的明确公式，并且还表明，对于相应的加权伯格曼核心，最有可能没有明确的（“封闭”）公式。
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.
