Professor Bercovici will study the properties of free additive and multiplicative convolution of measures in the convex plane, as well as applications of these operations to the calculation of spectral invariants. He will continue the study of spectral versions of the Nevanlinna-Pick, Caratheodory, and Nehari problems and explore their relations with control theory. Another topic of study will be the structure of dual algebras with an emphasis on algebras generated by a finite number of commuting operators. Professor Bercovici's research concerns operators on Hilbert space. Hilbert space operators are essentially infinite matrices of complex numbers. These operators have applications in every area of applied science as well as in pure mathematics. Research of this type is an attempt to classify certain important families of such operators.
