Representation of the inverse of a frame multiplier

• DOI: 10.1016/j.jmaa.2014.09.020
• Publication Date: 2014-09-16T10:41:54Z
• Authors: P. Balazs; D.T. Stoeva
• Keywords: Representation

Certain mathematical objects appear in a lot of scientific disciplines, like physics, signal processing and, naturally, mathematics. In general setting they can be described as frame multipliers, consisting analysis, multiplication by fixed sequence (called the symbol), and synthesis. this paper we show surprising result about inverse such operators, if any, well new results core concept theory, dual frames. We that for semi-normalized symbols, any invertible multiplier always represented with reciprocal symbol frames given ones. Furthermore, one those is uniquely determined other arbitrarily chosen. investigate sufficient conditions special case, when both chosen to canonical duals. connection above, set determines uniquely. frame, union all coefficients its dense [Formula: see text]. also introduce class pseudo-coherent frames), which includes Gabor coherent frames, allowing classification frame-type operators these Finally, give numerical example invertibility multipliers case.