Title: “Operator representations of frames and structured function systems”
Place: Thursday 22 November, 2018 at 13:00,The Technical University of Denmark, Building 308, Auditorium 12, 2800 Kgs. Lyngby
Principal supervisor: Professor Ole Christensen
Co-supervisor: Associate Professor Jakob Lemvig
Examiners:
Associate Professor Kim Knudsen, DTU Compute
Associate Professor Karl Grosse-Erdmann, University of Mons
Professor Morten Nielsen, Aalborg University
Chairman:
Associate Professor Kristian Uldall Kristiansen, DTU Compute
Summary: Typical results for representation and analysis of signals are obtained using frame theory. A particular and important role is played by the so-called structured function systems, e.g., Gabor systems and wavelet systems. While certain classes of signals are known to be treated most efficiently by either a Gabor system or a wavelet system, other signals have features that made it adventurous to use a combination of these systems. An appropriate class of systems for this purpose is formed by the so-called Generalizes shift-invariant systems (GSI-systems). One of the advantages of GSI-systems is that they apply to as well one-dimensional as higher-dimensional signals. The project will generalize some of the important results from Gabor/wavelet theory to the setting of GSI-systems, e.g., necessarily conditions in term of lower bounds of the Calderon sum.
For applications of frames to concrete signals, it is crucial to have efficient representations of the involved frames. A substantial part of the project will consist in the analysis of frames that can be represented using iterations of a single bounded operator. This part of the project connects frame theory with deep problems in operator theory.
READ MORE at orbit.dtu.dk
A copy of the PhD thesis is available for reading at the department.
Everyone is welcome.