4 papers
The classes of bivariate Schur and Herglotz matrix-valued rational functions: realizations, symmetrizations, and related determinantal representations
Radomił Baran, Piotr Pikul, Hugo J. Woerdeman +1
We present a finite-dimensional realization theory for bivariate rational functions that are contractive or have nonnegative real part on the bidisc or on the bihalfplane. We show…
The joint numerical range of three hermitian matrices
Piotr Pikul, Ilya Spitkovsky, Konrad Szymański +2
We analyze the joint numerical range of three hermitian matrices of order four. In the generic case, this three-dimensional convex set has a smooth boundary. We analyze non-gen…
Contractive realization theory for the annulus and other intersections of discs on the Riemann sphere
Radomił Baran, Piotr Pikul, Hugo J. Woerdeman +1
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 m…
The Szász inequality for matrix polynomials and functional calculus
Piotr Pikul, Oskar Jakub Szymański, Michał Wojtylak
The Szász inequality is a classical result that provides a bound for polynomials with zeros in the upper half of the complex plane, expressed in terms of their low-order coefficien…