Seminar: A Spline Frame Characterization for Sobolev Space

Thời gian: 9:00:01/01/0001 đến 10:30:09/07/2024

Địa điểm: Phòng B.102, VIASM

Báo cáo viên: Andrew Haar, Charles University, Prague, Czech Republic

Abstract:The Battle-Lemarié spline wavelet system has seen great success in its ability to characterize function spaces measuring smoothness. It is a classical fact that one can use it as a basis for Sobolev spaces so long as the smoothness parameter, s, is not too large. We will discuss how we can expand this permissible range for s by giving up the requirement that the system be a basis and instead create a frame from spline coefficients, which characterizes the Sobolev norm (in other words, we create this frame by oversampling against our spline system). In the process of the presentation, we will exploit a remarkable and novel connection between B-splines and the Battle-Lemarié system. We will also briefly discuss how each result extends to the more general Besov and Triebel-Lizorkin spaces.