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 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 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.