The two-by-two spectral Nevanlinna-Pick problem
Jim Agler and Nicholas Young
Keywords
mu-synthesis, interpolation, symmetrised bidisc
Status
Trans. Amer. Math. Soc. 356 (2004), 573-585 (available
electronically
on the Trans. AMS website).
Abstract
We give a criterion for the existence of an analytic two by two
matrix-valued function on the disc satisfying a finite set of
interpolation conditions and having spectral radius bounded by $1$. We also
give a realization theorem for analytic functions from the disc to the
symmetrised bidisc, defined to be the set
$$
\Gamma=\{(z_1 + z_2,\ z_1 z_2): |z_1|\le 1,\ |z_2|\le 1\}.
$$
J. Agler's work is suported by an NSF grant in Modern Analysis.
This work was also supported by an EPSRC Visiting Fellowship.
Nicholas Young
7th September, 2001.