Functional Analysis and Applications Seminar 

26/01/2007, 15:00 — 16:00 — Room P3.10, Mathematics Building
Teresa Malheiro, Universidade do Minho, Guimarães

Meromorphic factorization revisited and application to a group of matrices

It is shown that the $2\times 2$ symbols in a class of exponentials of nilpotent matrices can be reduced, by splitting some rational factors, to a very simple normal form. A meromorphic factorization [1] of these symbols is thus naturally defined and by approaching the problem of transforming it into a generalized factorization from a point of view different from that of [1], we study the invertibility and the Fredholm properties of the Toeplitz operators with symbols in that class. These results simplify and generalize those obtained in [2]. This is a joint work with Cristina Câmara, IST, Lisboa.

1. Câmara, M. C., Lebre, A., Speck, F.-O. Generalised factorisation for a class of Jones form matrix functions. Proc. Roy. Soc. Ed., 123A (1993) 401-422.
2. Câmara, M. C., Malheiro, M. T. Wiener-Hopf factorization for a group of exponentials of nilpotent matrices. Linear Algebra Appl. 320(1-3) (2000) 79-96.