Extension Problems under the Displacement Structure Regime. (Reannouncement withNew Availability Information)

摘要

This paper presents a unified approach to certain function-theoretic and matrixextension problems, which is based on the recently developed concept of matrices with a generalized displacement structure. We show that a variety of function extension problems, including Pad approximation and Caratheodory extension, are equivalent to the problem of extending a finite matrix with a given displacement structure into a larger (possible infinite) matrix with the same structure. Moreover, such matrix extension problems can be efficiently solved by the same layer-peeling procedure that is used to determine the triangular factorization of matrices with a generalized displacement structure.