Approximation properties and characterization of operator coorbit spaces

Lukas Köhldorfer (Acoustics Research Institute, Vienna)

May 08. 2025, 15:45 — 16:15

Recently, operator coorbit spaces have been introduced by Dörfler, Luef, McNulty and Skrettingland. A Hilbert-Schmidt operator on $L^2(\mathbb{R}^d)$ belongs to the operator coorbit space $\mathfrak{M}^p$, if and only if its operator short-time Fourier transform belongs to the Bochner $L^p$ space of measurable functions with values in the space of Hilbert-Schmidt operators on $L^2(\mathbb{R}^d)$. We show that the operator coorbit spaces $\mathfrak{M}^p$ coincide with the coorbit spaces associated with a certain polynomially localized g-frame for the space of Hilbert-Schmidt operators on $L^2(\mathbb{R}^d)$. Having this characterization available, we can derive approximation theoretic results for operator coorbit spaces.

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)