9500954 Putinar This project involves continued research in multivariable spectral theory and in the theory of hyponormal operators. In the first area, standard cohomological methods will be combined with hard analysis techniques of several complex variables in the study of a class of Hilbert modules over function algebras. In the second area, a novel correspondence between quadrature domains and hyponormal operators will be exploited and expanded in both directions. The research will focus on several new and not yet fully investigated relations between two areas of mathematical analysis: function theory and operator theory. The benefits are expected to be on both sides, with a great potential of further research and with applications to computational mathematics and quantum physics. ***
