Title: An uncertainty principle and its connection with quasi-analyticity.
Abstract: An Uncertainty principle due to Ingham provides the best possible decay of the Fourier transform of a function on \mathbb{R} which vanishes on a nonempty open set. To prove this result Ingham used the classical Denjoy-Carleman theorem for quasi-analytic functions on the real line. In this talk, we plan to discuss similar results in a more general context. To be precise, we will discuss an $L^2$-version of the Denjoy-Carelman theorem (due to Chernoff) and use this to prove the Ingham-type uncertainty principle for the (generalized) spectral projections associated with the Laplacian. To life less complicated, we will limit ourselves mainly to Euclidean spaces.
Termin
Dienstag, 20.12.2022
| 14.15 bis 15.30 Uhr
Oberseminar "Geometrische Analysis und Zahlentheorie": Pritam Ganguly (Universität Paderborn) -- hybrid
Veranstalter: D 1 320