Harmonic Analysis and Applications

June 4-8, 2018


"Formulas for the inversion of frame multipliers"

Stoeva, Diana

Frame multipliers are operators which consist of analysis with a frame, multiplication with a scalar sequence (called symbol or mask), and synthesis with a frame which might differ from the analysis-frame. Such type of operators, in particular Gabor frame multipliers, play an important role in signal processing. It is of interest both for applications and from pure operator theory point of view, to determine cases where multipliers are invertible and corresponding formulas for the inversion. In this talk, first we present sufficient conditions for the invertibility of multipliers and formulas for the inverses via Neumann-type series. Then we discuss representations of the inverses as multipliers based on appropriate dual frames of the initially given ones. In particular, we consider Gabor frame multipliers and cases where these appropriate dual frames also have a Gabor structure. The talk is based on a joint work with Peter Balazs.

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