Speaker
Michał Wojtylak
Description
A well known realisation theorem says that a rational matrix function, contractive on the disc, has a representationF(z) = D + C(I−zA)⁻¹B, with appropriately chosen matrices A,B,C,D such that the block matrix [A,B;C,D] is a contraction. A multivariate varsion of this result was obtained in [Grinshpan et al. 2016]. We will use that result to obtain a one-variable result for F(z) rational without poles in the annulus, or more general, in a multihole domain. The notion of contractivity needs to be adapted accordingly.
