@incollection{Lantzberg2013, author = {Lantzberg, Daniel}, title = {Rank-M Frame Multipliers and Optimality Criterions for Density Operators of Rank M}, series = {Current Trends in Aanalysis and Its Applications}, volume = {2015}, booktitle = {Current Trends in Aanalysis and Its Applications}, publisher = {Springer}, isbn = {978-3-319-12576-3}, doi = {10.1007/978-3-319-12577-0_76}, pages = {695 -- 704}, year = {2013}, abstract = {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.}, subject = {Mathematik}, language = {en} }