Invariances of the operator properties of frame multipliers under perturbations of frames and symbol

2016/08/21 by Hossein Javanshiri, Javanshiri, Hossein
Mathematics · #47A58 #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 42C15 #Secondary: 47A55 #math.FA #msc:42C15 #msc:47A55 #msc:47A58

paper · pdf · doi:10.48550/arxiv.1608.05929

arxiv created 2016/08/21 · arxiv updated 2016/08/23

Abstract

Let Φ and Ψ be frames for \cal H and let M_m,Φ,Ψ be a frame multiplier with the symbol m. In this paper, we restrict our investigation to show that the operator properties of M_m,Φ,Ψ are stable under the perturbations of Φ, Ψ and m. Also, special attention is devoted to the study of invertible frame multipliers. These results are not only of interest in their own right, but also they pave the way for obtaining some new results for Gabor multipliers which have been studied mostly by Hans Georg Feichtinger and his coauthors in recent years.

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