In this talk, we will take a look at a Benedicks-type uncertainty principle for a class of joint time-frequency representations, namely, metaplectic time-frequency representations. These joint representations arise from metaplectic operators and are a generalization of the short-time Fourier transform and the Wigner distribution.
Given a metaplectic time-frequency representation, we investigate whether there exist non-zero functions whose metaplectic time-frequency representation is supported on a set of finite measure. We study this both in the sesquilinear and the quadratic version and provide a full characterization of the class of metaplectic time-frequency representations which exhibit an uncertainty principle of this type.
This is joint work with K. Gröchenig (University of Vienna).
https://univienna.zoom.us/j/67922750549?pwd=Ulh5L1QxNFhBOC9PUjlVdG9hc0tmUT09