INTERPOLATION SUBMANIFOLDS OF THE UNITARY-GROUP

An interpolation subset in the boundary of a domain is a closed set in which every continuous (or smooth) function can be extended as a holo morphic function inside the domain and continuous (or smooth, respecti vely) up to the boundary. In this paper we give some geometric descrip tion for submanifolds in the unitary group to be interpolation sets fo r the domain obtained by taking polynomial hull of the unitary group. In particular, we retrieved corresponding results on the polydisc.