TY - CHAP A1 - Lantzberg, Daniel T1 - Rank-M Frame Multipliers and Optimality Criterions for Density Operators of Rank M T2 - Current Trends in Aanalysis and Its Applications N2 - Ever since the introduction of frames in 1952 [4], 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. KW - Frames KW - Multipliers KW - Operator Approximation KW - Locally Compact Groups KW - Uncertainty Principle KW - Mathematik KW - Aufsatzsammlung Y1 - 2013 SN - 978-3-319-12576-3 U6 - https://doi.org/10.1007/978-3-319-12577-0_76 VL - 2015 SP - 695 EP - 704 PB - Springer ER -