@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} } @phdthesis{Lantzberg2019, author = {Lantzberg, Daniel}, title = {Quantum Frames and Uncertainty Principles arising from Symplectomorphisms}, url = {http://nbn-resolving.de/urn:nbn:de:gbv:46-00107143-11}, school = {Technische Hochschule Aschaffenburg}, year = {2019}, subject = {Signalverarbeitung}, language = {en} } @article{StarkLiebLantzberg2013, author = {Stark, Hans-Georg and Lieb, Florian and Lantzberg, Daniel}, title = {Variance Based Uncertainty Principles and Minimum Uncertainty Samplings}, series = {Applied Mathematics Letters}, volume = {26(2013)}, journal = {Applied Mathematics Letters}, number = {2}, doi = {10.1016/j.aml.2012.08.009}, pages = {189 -- 193}, year = {2013}, subject = {Wavelet}, language = {en} } @inproceedings{LantzbergLiebStarketal.2012, author = {Lantzberg, Daniel and Lieb, Florian and Stark, Hans-Georg and Levie, Ron and Sochen, Nir}, title = {Uncertainty Principles, Minimum Uncertainty Samplings and Translations}, series = {Proceedings of the 20th European Signal Processing Conference (EUSIPCO) 2012, EURASIP}, booktitle = {Proceedings of the 20th European Signal Processing Conference (EUSIPCO) 2012, EURASIP}, isbn = {978-1-4673-1068-0}, issn = {2219-5491}, pages = {799 -- 803}, year = {2012}, subject = {Signalverarbeitung}, language = {en} }