An inverse entropy optimization problem for matrix-valued carathéodory functions

Abstract

In a landmark paper Arov and Krein studied entropy minimization problems over a set of matrix-valued Caratheodory functions which arises from a linear fractional transformation the generating matrix-valued function of which is a j _qq—J _q-inner function. Our paper handles the corresponding inverse problem: If a q x q Carath éodory function Ω is given, then the problem is to determine all j _qq—J _q-inner functions for which Omega; proves to be the associated entropy-minimal function

Keywords:

• Stationary Sequences
• Prediction Theory
• Inverse Entropy Optimization
• CarathéOdory Functions
• j _qq—J _q-Inner Functions