On the Bosonic Bergman Kernel in the Theory of Higher Spins
摘要
The notion of bosonic Laplacian, which is a correspondence of the Laplacian in the theory of higher spins, has been extensively studied in the framework of Clifford analysis. Recently, the concept of bosonic Bergman spaces has been introduced to generalize harmonic Bergman spaces to the theory of higher spins. In this article, we initiate the study of bosonic Bergman kernels. In particular, closed forms for the bosonic Bergman kernels in the unit ball and the upper-half space are provided.