Contractive realization theory for the annulus and other intersections of discs on the Riemann sphere

Abstract

We develop contractive finite dimensional realizations for rational matrix functions of one variable on domains that are not simply connected, such as the annulus. The proof uses multivariable contractive realization results as well as abstract operator algebra techniques. Other results include new bounds for the Bohr radius of the bidisk and the annulus.

arXiv comment20 pages, 2 figures