06/10/2017, 15:00 — 16:00 — Room P3.10, Mathematics Building
Bernd Silbermann, Technische Universität Chemnitz, Germany
On the spectrum of the Hilbert matrix operator
For each, $\lambda\in\mathbb{C}$, $\lambda\neq 0,-1,-2,...$ the (generalized) Hilbert matrix $\mathcal{H}_{\lambda}$ is given by $$\mathcal{H}_{\lambda}:=\left(\frac{1}{n+m+\lambda}\right)_{n,m\geq0}.$$ If $\lambda=1$ then $\mathcal{H}_{\lambda}$ is the classical Hilbert matrix introduced by D. Hilbert about 125 years ago. These matrices have been the subject of numerous investigations. The talk mainly concerns the description of spectral properties of Hankel operators generated by these matrices on the Hardy spaces $H^{p}$ and $l^{p}$ $(1 < p < \infty$). Special attention will be paid to the description of the essential and point spectra of these operators.
