G. Groenewald

collaborators

3 papers

math.FA2024

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 $H^{p}$ and Bergman spaces $A^{p}$ , $1<p…

math.FA2024

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 $p (z) = p (z_{1}, \dots, z_{d})$ with a determinantal representation $p (z) = p (0) det (I_{n} - K (\oplus_{j = 1}^{d} z_{j} I_{n_{j}}))$ the matrix $…

math.FA2024

A Toeplitz-like operator with rational matrix symbol having poles on the unit circle:\ Matrix representation and spectral analysis

G. J. Groenewald, S. ter Horst, J. Jaftha +1

In this paper we consider a class of unbounded Toeplitz operators with rational matrix symbols that have poles on the unit circle and employ state space realization techniques from…