ﻻ يوجد ملخص باللغة العربية
In this paper we study two design problems in frame theory: on the one hand, given a fixed finite frame $cF$ for $hilcongC^d$ we compute those dual frames $cG$ of $cF$ that are optimal perturbations of the canonical dual frame for $cF$ under certain restrictions on the norms of the elements of $cG$. On the other hand, for a fixed finite frame $cF={f_j}_{jinIn}$ for $hil$ we compute those invertible operators $V$ such that $V^*V$ is a perturbation of the identity and such that the frame $Vcdot cF={V,f_j}_{jinIn}$ - which is equivalent to $cF$ - is optimal among such perturbations of $cF$. In both cases, optimality is measured with respect to submajorization of the eigenvalues of the frame operators. Hence, our optimal designs are minimizers of a family of convex potentials that include the frame potential and the mean squared error. The key tool for these results is a multiplicative analogue of Lidskiis inequality in terms of log-majorization and a characterization of the case of equality.
In this paper we consider two problems in frame theory. On the one hand, given a set of vectors $mathcal F$ we describe the spectral and geometrical structure of optimal completions of $mathcal F$ by a finite family of vectors with prescribed norms,
In 2012 Gu{a}vruc{t}a introduced the notions of $K$-frame and of atomic system for a linear bounded operator $K$ in a Hilbert space $mathcal{H}$, in order to decompose its range $mathcal{R}(K)$ with a frame-like expansion. In this article we revisit
Bell inequalities are important tools in contrasting classical and quantum behaviors. To date, most Bell inequalities are linear combinations of statistical correlations between remote parties. Nevertheless, finding the classical and quantum mechanic
In this paper we obtain quite general and definitive forms for Hardy-Littlewood type inequalities. Moreover, when restricted to the original particular cases, our approach provides much simpler and straightforward proofs and we are able to show that
We introduce the concept of weak-localization for generalized frames and use this concept to define a class of weakly localized operators. This class contains many important operators, including: Short Time Fourier Transform multipliers, Calderon-Toe