Functional Analysis and Applications Seminar 

16/06/2006, 15:00 — 16:00 — Room P3.10, Mathematics Building
Cristina Diogo, Instituto Superior Técnico, U.T. Lisboa

Generalized factorization for a class of triangular symbols with a gap around zero

It was shown in [1] that if a bounded analytic solution to the Riemann-Hilbert problem $G h_+ = h_-$ is known which consists of corona pairs, then $G$ admits a canonical generalized factorization, i.e., the Toeplitz operator with symbol $G$ is invertible. But what if the solution does not satisfy the corona conditions? And, to begin at the beginning, how to get a particular bounded analytic solution to the Riemann-Hilbert problem? We adress these questions by studying a class of triangular matrix symbols which illustrates the problems involved in those questions and for which we can find answers.

1. Bastos, M. A., Karlovich, Y. I. and dos Santos, A. F., Oscillatory Riemann-Hilbert problems and corona theorem, Journal of Functional Analysis 197 (2003) 347-397.