The Schur Problem and Block Operator CMV Matrices

Abstract

The CMV matrices and their sub-matrices are applied to the description of all solutions to the Schur interpolation problem for contractive analytic operator-valued functions in the unit disk (the Schur class functions).

Poncelet's theorem, paraorthogonal polynomials and the numerical range of compressed multiplication operators

“…Arlinski ǐ has four papers [1,2,3,4], one with coauthors, that are related to the above three theorem. These papers deal with a related, but different, class of operators which he calls truncated CMV matrices.…”

“…Marden's 1948 book [49,Ch. 1,§4], Geometry of Polynomials, popularized a theorem which he traces back to an 1864 paper of Jörg Siebeck [57].…”