Functional Analysis and Applications Seminar 

28/05/2010, 14:30 — 15:30 — Room P3.10, Mathematics Building
Ana C. Conceição and José C. Pereira, Universidade do Algarve, Faro

Explicit generalized factorization with Mathematica 6.0

The aim of this seminar is to present our progress in the explicit generalized factorization of some special matrix-valued functions. We construct an algorithm to obtain the solutions of certain singular integral equations related with a self-adjoint operator. Using these solutions we construct another algorithm to determine an effective factorization of the matrix functions. Using Mathematica 6.0 symbolic computation package we implement the two algorithms on a digital computer, automating the factorization process as a whole. We present some examples, both in the real line and in the unit circle, obtained with the Mathematica application. The presentation is based on a joint work with Viktor G. Kravchenko.