Treil and Peller will continue their work on Hankel operators and their applications. In particular, they will investigate spectral properties of self-adjoint Hankel operators and their relations with balanced realizations with continuous time and with discrete time; spectral characterizations of the completely regular vectorial stationary random processes; superoptimal approximations of matrix-valued functions; and special approximation by finite rank Hankel operators that repeat first singular values of the initial operator. 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.
