M. Putinar and F. H. Vasilescu, “Solving Moment Problems by Dimensional Extension,” Annals of Mathematics, Vol. 148, No. 3, 1999, pp. 1087-1107.

has been cited by the following article:

• TITLE: Positive-Definite Operator-Valued Kernels and Integral Representations

  AUTHORS: L. Lemnete-Ninulescu

  KEYWORDS: Unitary-Operator; Self-Adjoint Operator; Joint Spectral Measure of a Commuting Tuple of Operators; Spectral Projector; Complex Moments; Analytic Vectorial Functions

  JOURNAL NAME: Applied Mathematics, Vol.3 No.12, December 24, 2012

  ABSTRACT: 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.