Integral formulas and problems of holomorphic extension from the boundary in Siegel domains

The purpose of this study is to construct an analogue of the Cayley transform for matrix domains, to describe the automorphism groups of Siegel domains, to obtain explicit formulas for the kernels of the Bergman, Cauchy—Szegő, and Poisson integrals, and to establish sufficient conditions for holomorphic extension from the boundary of a Siegel domain in the form of Morera-type theorems.