Abstract
We present results about minimization of convex functionals defined over a finite set of vectors in a finite-dimensional Hilbert space, that extend several known results for the Benedetto-Fickus frame potential. Our approach depends on majorization techniques. We also consider some perturbation problems, where a positive perturbation of the frame operator of a set of vectors is realized as the frame operator of a set of vectors which is close to the original one.
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Communicated by QiYu Sun.
Partially supported by CONICET (PIP 5272) and UNLP (11 X472).
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Massey, P., Ruiz, M. Minimization of convex functionals over frame operators. Adv Comput Math 32, 131–153 (2010). https://doi.org/10.1007/s10444-008-9092-5
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DOI: https://doi.org/10.1007/s10444-008-9092-5