Another project has investigated the basic properties of frame and Bessel multipliers. This project aims to generalize this concept so that it will work with Banach spaces also.
As the Gram matrix plays an important role in the investigation of multipliers, it is quite natural to look at the connection to localized frames and multipliers. The dependency of the operator class on the symbol class can be researched.
The following statements will be investigated:
The applications of these results to Gabor frames and Gabor multipliers will be further investigated.
Although Banach spaces are more general a concept than Hilbert spaces, Banach theory has found applications. For example, if any norm other than L2 (least square error) is used for approximation, Banach theory tools have to be applied.
This project ended on 28.02.2008 and is incorporated into the 'High Potential'-Project of the WWTF, MULAC.