9401848 Spitkovsky The project involves work on operator theory and matrix theory. Five specific projects are outlined: 1. Fredholm theory of Toeplitz, Weiner-Hopf and pseudodifferential operators on spaces with general Hunt-Muckenhoupt-Wheeden weights. Almost periodic factorization of matrix functions and its applications to extension and interpolation problems of Analysis. 3. Explicit solutions of integral equations and boundary problems emerging from applications to diffraction theory, elasticity and thermodynamics. 4. Further analysis of the structure of Banach algebras generated by two projections. 5. Contragredient canonical forms of pairs of Hermitian matrices and their applications. The project centers around the theory of systems of singular integral equations. Historically, these equations grew out of the study of the equation of the airfoil and other applications in the mechanics of materials. The basic tool for solving these singular integral equations is the method of Wiener-Hopf factorization. The matrix form of this factorization was developed independently by electrical engineers to study linear systems theory. A part of the project deals with explicit factorization and this would have application in engineering problems. When completed, the theoretical portion of the project will be a significant advance in the theory of matrix function factorization. ***
