Uncertainty principle, concentration of smooth functions and sampling

Mardi 8 décembre 2015 14:00-15:00 - Eugenia Malinnikova - Norwegian University of Science and Technology (NTNU, Trondheim)

Résumé : The classical Heisenberg uncertainty inequality shows that a function in the Sobolev space $H^1$ can be localized near some some point only if the ratio of the $L^2$-norm of its derivative and the norm of the function is large. In 1980s Strichartz obtained a number of uncertainty inequalities, his starting point was a sampling inequality for functions in the Sobolev space over a discrete sequence of points. We follow the idea of Strichartz and prove uncertainty inequalities that connect the concentration of the function on some suitably uniformly distributed subset to the norm of the function in some Besov space. The results are connected to the classical trace theorems for functions in Besov spaces and can be applied to non-regular sampling. The talk is based on a joint work with Ph. Jaming

Lieu : Salle 113-115 (Bâtiment 425)

Uncertainty principle, concentration of smooth functions and sampling  Version PDF