Mathematisches Forschungskolloquium 2022
- Prof. Dr. Hajo Holzmann (Philipps-Universität Marburg)
"Statistical Analysis of Time-Frequency Methods"
Abstract: Time-frequency analysis deals with signals for which the underlying spectral characteristics change over time. The essential tool is the short-time Fourier transform, which localizes the Fourier transform in time by means of a window function. In a white noise model, we derive rate-optimal and adaptive estimators of signals in modulation spaces, which measure smoothness in terms of decay properties of the short-time Fourier transform. The estimators are based on series expansions by means of Gabor frames and on thresholding the coefficients. The minimax rates have interesting new features, and the derivation of the lower bounds requires the use of test functions which approximately localize both in time and in frequency. Simulations and applications to audio recordings illustrate the practical relevance of our methods. Der Vortrag basiert auf der Arbeit
13. Oktober 2022, 17:00 Uhr, HS 125 (Ulmenstr. 69, Haus 3)
Kolloquiumsleiter: Prof. Dr. Alexander Meister
- Prof. Dr. i.R. Friedemann Brock (Univ. Leipzig/Halle/Rostock)
"Symmetry and stability of non-negative solutions to degenerate elliptic equations in a ball"
01. March 2022, 14:00 Uhr, Online event via Zoom
Kolloquiumsleiter: Prof. Dr. Peter Takac, Ph.D.