HAMBURGER MOMENT PROBLEM - PARSEVAL EQUALITY AND A-SINGULARITY

In one of the author's previous papers, the ''Parst val Equality'' was established for any A-regular scattering operator function (i.e., for one associated with the Generalized Bitangential Schur-Nevanlinna-Pic k Problem), The infinite Hamburger Moment Problem gives an example of an A-singular scattering operator-function with the ''Parseval Equalit y'' property. This leads to a negative answer to a question due to V. M. Adamjan, D. Z. Arov, and M. Cr. Krein, and (what is the same) produ ces a counter-example to D. Sarason's conjecture concerning exposed po ints in H-1. (C) 1996 Academic Press, Inc.