Project: In this project we aim to generalize various results on Gabor frames in one dimensional setting to the case of several dimensions. Our leading example is the Gaussian function in two dimensions which we shift by some general lattice, and we want to find necessary and sufficient conditions on this lattice so that the resulting system is a frame. We are also interested in more general window functions, in particular rational functions of several variables, as well as more general sets of shifts, for example by a finite union of different lattices. These problems are deeply related to sampling problems in certain shift-invariant spaces, and we plan to employ this connection in our work.

Research Team: Prof. Karlheinz Gröchenig (University of Vienna), Dr. Aleksei Kulikov (University of Copenhagen), Prof. Alexander Ulanovskii (University of Stavanger), Dr. Ilia Zlotnikov (Norwegian University for Science and Technology)

Dates of Stay: April 6 - May 5, 2026