Codes and Expansions (CodEx) Seminar
John J. Benedetto (University of Maryland)
Spectral super-resolution and unique extensions for complex measures
Spectral data will designate the Fourier transform of a complex measure. We motivate the essential role in spectral super-resolution of proving unique extensions to the whole space from given spectral data on subsets. The subsets we consider are Yves Meyer's model sets associated with quasi-crystals. Our results begin with Matei's basic theorem in the area. Besides Meyer's Poisson summation formula and Kronecker's theorem, our approach requires a new direction and extension of Chebotarëv's theorem.
This is a collaboration with Chenzhi Zhao.