Abstract
In this paper, we consider the determinant of the multivariable return difference Nyquist map, crucial in defining the complex /spl mu/-function, as a holomorphic function defined on a polydisk of uncertainty. They key property of holomorphic functions of several complex variables that is crucial in our argument is that it is an open mapping. From this single result only, we show that, in the diagonal perturbation case, all preimage points of the boundary of the Horowitz template are included in the distinguished boundary of the polydisk. In the block-diagonal perturbation case, where each block is norm-bounded by one, a preimage of a boundary point is shown to be a block unitary matrix. Finally, some algebraic geometry, together with the Weierstrass preparation theorem, allows us to show that the deformation of the crossover under (holomorphic) variations of "certain" parameters is continuous.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.