Hermitian-Positive Functions of Several Variables

Abstract

The Hermitian-positive functions play an essential role in a number of analysis problems (probability theory [47], inverse spectral problem [53] interpolation problems [53]). In many of these problems it becomes necessary to extend the Hermitian-positive functions onto a greater domain with the preservation of Hermitian positiveness. For the Hermitian-positive functions of one variable the extension problem was formulated and solved in the classical works by M.Krein [32] (see section 1.7). The extension problem of Hermitian-positive functions of two and more variables has been investigated much less.