Functional Analysis and Applications Seminar 

11/02/2011, 15:00 — 16:00 — Room P3.10, Mathematics Building
Alexei Karlovich, Universidade Nova de Lisboa and Centro de Análise Funcional e Aplicações, IST

Singular integral operators with shifts and slowly oscillating data

Suppose we are given an orientation preserving diffeomorphism (shift) of the semi-axis onto itself with the only fixed points zero and the point at infinity. We establish Fredholmn criteria for a class of singular integral operator with shift under the assumptions that the coefficients and the derivative of the shift are bounded and continuous on the open semi-axis and may admit discontinuities of slowly oscillating type at zero and at infinity. In this talk we briefly discuss the proof of the sufficiency part (presented at WOTCA 2010) and give a more detailed account on the proof of the necessity part. This talk is based on the joint work with Yuri Karlovich and Amarino Lebre.