Truncated Hamburger moment problem for an operator measure with compact support

Abstract

AbstractGiven bounded selfadjoint operators \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$F_1=I_{\mathfrak N}$\end{document}, F2, …, F2n + 1 in a separable Hilbert space \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathfrak N$\end{document}, we consider the operator truncated Hamburger moment problem of finding a Herglotz‐Nevanlinna operator‐valued function M holomorphic in the neighborhood of infinity and having the form Criteria of the solvability and uniqueness of the solution are established and a description of all solutions is obtained. Our approach is based on the Schur transformation, the Schur parameters, and the special block operator Jacobi matrices.