Abstract
Ever since the introduction of frames in Duffin and Schaeffer (Trans. Am. Math. Soc. 72:341–366, 1952), the connection between frame theory and decompositions of certain operators, particularly the identity operator, into rank-ones began to be elaborated. Abandoning the idea of restricting to tight frame-like expansions, with respect to systems arising from a single template function, one is led to the concept of resolutions of the identity, with respect to more general systems than the usual rank-one expansions of the identity.
In this study, we will investigate various notions of possible generalizations of optimality criterions for rank-M frames and corresponding multipliers. Explicitly, we will lay stress on continuous M-frames, arising from irreducible group representations of locally compact groups, have a look at its connection to time-frequency analysis and comment on adequate notions of optimality.
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Acknowledgement
The author gratefully acknowledges the suggested improvements by the referee. This research has been (partially) supported by EU FET Open grant UNLocX (255931).
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Lantzberg, D. (2015). Rank-M Frame Multipliers and Optimality Criterions for Density Operators of Rank M. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_76
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DOI: https://doi.org/10.1007/978-3-319-12577-0_76
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