Localized Frames and Compactness |
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Authors: | Fawwaz Batayneh Mishko Mitkovski |
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Institution: | 1.Department of Mathematical Sciences,Clemson University,Clemson,USA |
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Abstract: | We introduce the concept of weak localization for continuous frames and use this concept to define a class of weakly localized operators. This class contains many important classes of operators, including: short time Fourier transform multipliers, Calderon–Toeplitz operators, Toeplitz operators on various functions spaces, Anti-Wick operators, some pseudodifferential operators, some Calderon–Zygmund operators, and many others. In this paper, we study the boundedness and compactness of weakly localized operators. In particular, we provide a characterization of compactness for weakly localized operators in terms of the behavior of their Berezin transforms. |
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