Hermitian-Positive Functions of Several Variables
The Hermitian-positive functions play an essential role in a number of analysis problems (probability theory , inverse spectral problem  interpolation problems ). 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  (see section 1.7). The extension problem of Hermitian-positive functions of two and more variables has been investigated much less.
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