Linear Analysis of Quadrature Domains, III

matricial structure of all hyponormal operators with finite rank self-commutators, which is inductively constructed from such linear data, is discussed. In particular, a conservation law (of a determinantal function) in the iterative process of defining these matrices is exploited. The spectrum of the determining left upper corner of some of these operators is analyzed in connection with the existence of generalized quadrature formulas on planar domains.