Maximum Entropy Interpolants and Maximum Determinant Completions of Associated Pick Matrices.

Classes of (n+k) by (n+k) completions of a given n by n positive definite matrix are considered. Explicit formulas are obtained for the completion which maximizes the determinant in each class. The results are then interpreted in terms of the solution of an associated interpolation problem which maximizes an entropy integral.

The talk will be largely expository. It is based in part on a joint paper with I. Gohberg.

Prof Harry Dym, Department of Theoretical Mathematics, The Weizmann Institute of Science, Rehovot, Israel