25/07/2003, 14:00 — 16:00 — Sala P3.10, Pavilhão de Matemática
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.