Functional Analysis and Applications Seminar 

25/07/2003, 14:00 — 16:00 — Room P3.10, Mathematics Building
Yu. I. Karlovich, Universidad Autónoma del Estado de Morelos, México

An Algebra of Pseudodifferential Operators with Symbols of Restricted Smoothness

The talk is devoted to an algebra of pseudodifferential operators with presymbols which slowly oscillate with respect to the contour variable and are continuous functions of bounded total variation with respect to the dual variable. Boundedness and compactness conditions for such operators are obtained. A symbol calculus is constructed on the basis of an appropriate approximation of the presymbols by infinitely differentiable functions and by use of the techniques of oscillatory integrals. An isomorphism between the Banach algebra of pseudodifferential operators and their symbols is established. A Fredholm theory for the pseudodifferential operators under consideration is developed.