Putinar will investigate two sets of problems. The first concerns Toeplitz operators on multivariable Bergman spaces and their relevance for the function theory of several complex variables. He will relate the spectral problems for this class of operators to the theory of functions in pseudoconvex domains with L2-growth control at the boundary. The second set of problems is related to the theory of moments in Euclidean n- space. Putinar will try to determine methods for solving certain moment problems on semialgebraic subsets by using specific operator theories. Operator theory is that part of mathematics that studies the infinite dimensional generalizations of matrices. In particular, when restricted to finite dimensional subspaces, an operator has the usual linear properties, and thus can be represented by a matrix. The central problem in operator theory is to classify operators satisfying additional conditions given in terms of associated operators (e.g. the adjoint) or in terms of the underlying space. Operator theory underlies much of mathematics, and many of the applications of mathematics to other sciences.