6 papers
Hereditary NC Polynomials & Positivity Domains
Abdellah Islam, Jurij Volčič, Hugo J. Woerdeman
Noncommutative polynomials, elements of the free algebra generated by several noncommuting variables , are of importance in noncommutative algebra, fre…
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…
Symmetric Schur-class functions on the bidisk and Schur-class functions on the symmetrized bidisk
Radomił Baran, Hugo J. Woerdeman
We present some thoughts on the relation between symmetric Schur-class functions on the bidisk and Schur-class functions on the symmetrized bidisk. Among other things, use of this…
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…
Optimal interpolation in Hardy and Bergman spaces: a reproducing kernel Banach space approach
Gilbert J. Groenewald, Sanne ter Horst, Hugo J. Woerdeman
After a review of the reproducing kernel Banach space framework and semi-inner products, we apply the techniques to the setting of Hardy spaces and Bergman spaces , $1<p…
Indefinite determinantal representations versus nonsingularities on the noncommutative d-torus
Gilbert J. Groenewald, Sanne ter Horst, Hugo J. Woerdeman
We show that for a multivariable polynomial with a determinantal representation the matrix $…