%0 Journal Article
%T Positive-Definite Operator-Valued Kernels and Integral Representations
%A L. Lemnete-Ninulescu
%J Applied Mathematics
%P 1990-1999
%@ 2152-7393
%D 2012
%I Scientific Research Publishing
%R 10.4236/am.2012.312274
%X A truncated trigonometric, operator-valued moment problem in section 3 of this note is solved. Let   be a finite sequence of bounded operators, with   arbitrary, acting on a finite dimensional Hilbert space H. A necessary and sufficient condition on the positivity of an operator kernel for the existence of an atomic, positive, operator-valued measure  , with the property that for every   with  , the   moment of   coincides with the   term   of the sequence, is given. The connection between some positive definite operator-valued kernels and the Riesz-Herglotz integral representation of the analytic on the unit disc, operator-valued functions with positive real part in the class of operators in Section 4 of the note is studied.
%K Unitary-Operator
%K Self-Adjoint Operator
%K Joint Spectral Measure of a Commuting Tuple of Operators
%K Spectral Projector
%K Complex Moments
%K Analytic Vectorial Functions
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=25642