Spectral deviation of Toeplitz operators on vector-valued reproducing kernel Hilbert spaces

Michael Speckbacher (Acoustics Research Institute, Vienna)

May 05. 2025, 14:00 — 14:30

In this talk, we build on the work of Marceca and Romero and study the eigenvalue distribution of Toeplitz operators on vector-valued reproducing kernel Hilbert spaces defined on rather general metric measure spaces. We provide estimates of how much the corresponding eigenvalue counting function deviates from the measure of the concentration domain. In this setting, the reproducing kernel is a Hilbert-Schmidt operator and our estimates crucially depend on the off-diagonal decay of Hilbert-Schmidt norm of the kernel. We then show how to apply the results to obtain estimates for the intermediate eigenvalues of mixed-state localization operators, localization operators based on the notion of the short-time Fourier transform with operator window, and Gabor multipliers.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Quantum Harmonic Analysis (Workshop)
Organizer(s):
Markus Faulhuber (U of Vienna)
Hans G. Feichtinger (U of Vienna)
Franz Luef (NTNU, Trondheim)