Functional Analysis and Applications Seminar 

14/11/2008, 15:15 — 16:15 — Room P3.10, Mathematics Building
Luís Castro, Universidade de Aveiro, Portugal

Solvability of singular integro-differential equations with multiple complex shifts

We will consider initial value problems for functional equations on the half-axis that contain Hilbert transforms, derivatives and complex shifts. The class of problems is motivated by various applications, and will be considered in both Bessel potential and Sobolev–Slobodeckij space settings. Results are Fredholm and invertibility criteria as well as explicit analytical solution in cases where techniques for the constructive factorization of symbol matrices are available. The talk is based on a joint work with R. Duduchava and F.-O. Speck.