arXiv subjects

Maria T. Nowak

Publications and source records attributed to Maria T. Nowak.

2 recordsLinked to original sources

arXiv2020

On kernels of Toeplitz operators

We apply the theory of de Branges-Rovnyak spaces to describe kernels of some Toeplitz operators on the classical Hardy space $H^2$. In particular, we discuss the kernels of the operators $T_{\bar f/ f}$ and $T_{\bar I\bar f/ f}$, where $f$ is an outer function in $H^2$ and $I$ is inner such that $I(0)=0$. We also obtain results on de Branges-Rovnyak spaces generated by nonextreme functions.

math.FA↗

arXiv2018

Examples of de Branges-Rovnyak spaces generated by nonextreme functions

We describe de Branges-Rovnyak spaces $\mathcal H (b_α)$, $α>0$, where the function $b_α$ is not extreme in the unit ball of $H^{\infty}$ on the unit disk $\mathbb D$, defined by the equality $b_α(z)/a_α(z)=(1-z)^{-α}$, $z\in\mathbb D$, where $a_α$ is the outer function such that $a_α(0)>0$ and $|a_α|^2+|b_α|^2= 1$ a.e. on $\partial \mathbb D$.

math.FA↗