21/04/2006, 14:30 — 16:00 — Room P3.10, Mathematics Building
Cristina Câmara, Instituto Superior Técnico, U.T. Lisboa
Fredholmness and corona problems
The Fredholm properties of Toeplitz operators with \(2\times 2\)
matrix symbols \(G\), which are essentially bounded on the real
line, are studied in connection with some properties of a solution
to a homogeneous linear Riemann-Hilbert problem with coefficient
\(G\). Conditions for the Toeplitz operator to be Fredholm are
obtained and, if that is the case, formulas for the factors in a
generalized factorization of \(G\) are given in terms of the
solutions to a pair of non-standard corona problems. These results
are used to establish partial index estimates for Daniele-Khrapkov
matrix functions.