Speaker
Eugenia Malinnikova, Stanford and NTNU
Abstract
We call a measurable subset of the real line “thick” if the measure of its intersection with any interval of length one is bounded from below. The classical theorem of Logvinenko and Sereda states that if the Fourier transform of a function is bounded, then the function itself can be (quantitatively) sampled from a thick set. In this talk, we will consider Schrödinger operators with increasing potentials and corresponding linear combinations of eigenfunctions with bounded eigenvalues. We will present spectral inequalities that provide estimates for sampling such linear combinations from (relatively) thick sets. The main tool is a new sharp Cauchy uniqueness estimate for solutions to a class of Schrodinger equations on the plane. The talk is based on a joint work with Jiuyi Zhu