ForschungAngewandte AnalysisOS Analysis und Theoretische Physik
Oberseminar Analysis und Theoretische Physik

Oberseminar Analysis und Theoretische Physik

Online-Vortrag, Dienstag 25.01.2022, 15:00 Uhr, Prof. Dr. Jani Virtanen (University of Reading und University of Helsinki), Compactness and Schatten class properties of Hankel operators on Fock spaces, and applications to the Berezin-Toeplitz quantization

Compactness and Schatten class properties of Hankel operators on Fock spaces, and applications to the Berezin-Toeplitz quantization

Using the space IDA of locally integrable functions whose integral distance to holomorphic functions is finite, we characterize boundedness, compactness and Schatten class membership of Hankel operators on weighted Fock spaces. As an application, for bounded symbols f, we show that the Hankel operator Hf is compact (or in the Schatten class Sp) if and only if H ̄f is compact (or H ̄f is in Sp), which complements the classical compactness result of Berger and Coburn and extends Bauer’s result on Hilbert-Schmidt Hankel operators. We also apply our results to the Berezin-Toeplitz quantization and answer a related question of Bauerand Coburn.

Joint work with Zhangjian Hu.