Hamburger Moment Problem: Parseval Equality andA-Singularity

Abstract

AbstractIn one of the author's previous papers, the “Parseval Equality” was established for anyA-regular scattering operator function (i.e., for one associated with the Generalized Bitangential Schur–Nevanlinna–Pick Problem). The infinite Hamburger Moment Problem gives an example of anA-singular scattering operator-function with the “Parseval Equality” property. This leads to a negative answer to a question due to V. M. Adamjan, D. Z. Arov, and M. G. Krein, and (what is the same) produces a counter-example to D. Sarason's conjecture concerning exposed points inH1