Kernels of Toeplitz operators
Kernels of Toeplitz operators
Let $U$ be the open unit disc in the complex plane and let $\partial U$ be the boundary of $U$ .If $f$ is analytic in $U$ and $\int_{-r}^{\pi}\log^{+}|f(re^{i\theta})|d\theta$ is bounded for $0\leqq r<1$ , $f(e^{i\theta})$ , which we define to be $\lim_{rarrow 1}f(re^{i\theta})$ , exists almost everywhere on $\partial U$ …