Abstract
Toeplitz operators on Hardy spaces $H\sp{p} $ have been studied extensively during the past 40 years or so. An important special case is that of the operators of multiplication by a bounded analytic function $\f $: $M\sb{\f}(f)=\f f $ (analytic Toeplitz operators). However, many results about them are either only formulated in the case $p=2 $, or are not so easy to find in an explicit form. The purpose of this paper is to give a complete overview of the spectral theory of these analytic Toeplitz operators on a general space $H\sp{p} $, $1\le p <\infty $. The treatment is kept as elementary as possible, placing a special emphasis on the key role played by certain extremal functions related to the Poisson kernel.
Citation
Dragan Vukotić. "Analytic Toeplitz operators on the Hardy space $H^p $: a survey." Bull. Belg. Math. Soc. Simon Stevin 10 (1) 101 - 113, January 2003. https://doi.org/10.36045/bbms/1047309417
Information