Functional Analysis and Applications Seminar 

17/05/2002, 14:00 — 15:00 — Room P3.10, Mathematics Building
Frank-Olme Speck, Instituto Superior Técnico, U.T.L.

Transformation Techniques towards the Factorization of Non-Rational 2 x 2 Matrix Functions

For the Wiener-Hopf factorization of $2\times 2$ matrix functions defined on a closed Carleson curve, so-called rational transformations, i.e. multiplication by rational matrix functions, are important. In the first part of the lecture, the topic will be motivated by a variety of applications and by general operator theoretical facts as well. Then we establish a classification scheme for $2\times 2$ matrix functions, which is based on such transformations. We determine invariants under these transformations and describe those matrix functions which can be transformed to triangular or Daniele-Khrapkov form. In the third part we consider special rational transformations and study the same problem. For instance, we consider transformations with matrix functions that are analytic and invertible on an open neighborhood of the given curve.

The talk is based upon common work with Torsten Ehrhardt, to be published in Linear Algebra and Its Applications under the same title.