A maximum entropy principle for contractive interpolants
In this paper a maximum entropy principle is established for a class of continuous contractive \(m\times n\) matrix valued functions g with preassigned Fourier coefficients \(g_ j=\gamma_ j\) for \(j=0,1,... \). The function g in this class which achieves the maximum entropy is characterized in a number of different ways and its entropy is computed in terms of a Hankel operator based on the prescribed matrices \(\gamma_ 0,\gamma_ 1,... \). A pair of seemingly new Szegö type formulas are obtained enroute and some applications to Nevanlinna-Pick interpolation are indicated.
scientific article; zbMATH DE number 3944590
scientific article