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Mathematische Annalen, ISSN 0025-5831, 2/2019, Volume 373, Issue 1, pp. 643 - 677
We formulate and prove finite dimensional analogs for the classical Balian–Low theorem, and for a quantitative Balian–Low type theorem that, in the case of the... 
Mathematics, general | Mathematics | 42A38 | 39A12 | 42C15 | MATHEMATICS | Naturvetenskap | Natural Sciences | Matematik
Journal Article
Bollettino dell'Unione Matematica Italiana, ISSN 1972-6724, 12/2017, Volume 10, Issue 4, pp. 637 - 647
In this paper we study stability of multivariate wave packet frames. Necessary and sufficient conditions for a certain system to be multivariate wave packet... 
Frames | Stability | 42C30 | Mathematics, general | Wave packet system | Mathematics | 42C15
Journal Article
Journal of the London Mathematical Society, ISSN 0024-6107, 02/2020, Volume 101, Issue 1, pp. 393 - 431
We consider sets of trace‐normalized non‐negative operators in Hilbert–Schmidt balls that maximize their mutual Hilbert–Schmidt distance; these are optimal... 
81P45 (primary) | 52C17 (secondary) | 52A40 | 42C15 | 05B05 | MATHEMATICS | COMPLEX CODEBOOKS | MUTUALLY UNBIASED BASES | CODES | CONSTRUCTION | SYSTEMS | EQUIANGULAR TIGHT FRAMES | LINES
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 02/2017, Volume 272, Issue 3, pp. 1121 - 1146
Let A be a normal operator in a Hilbert space H, and let G⊂H be a countable set of vectors. We investigate the relations between A, G and L that make the... 
Sampling | Frames | Dynamics | MATHEMATICS | MULTIPLICITY | RECONSTRUCTION | SIGNALS | SYSTEMS | SUBSPACES | KADISON-SINGER PROBLEM | GABOR FRAMES
Journal Article
Constructive Approximation, ISSN 0176-4276, 2/2012, Volume 35, Issue 1, pp. 21 - 72
Shearlet tight frames have been extensively studied in recent years due to their optimal approximation properties of cartoon-like images and their unified... 
Curvilinear discontinuities | Shearlets | 65T99 | Mathematics | Edges | Optimal sparsity | Scaling functions | Wavelets | Filters | 42C40 | 94A08 | Analysis | Numerical Analysis | 42C15 | 65T60 | Nonlinear approximation | MATHEMATICS | Universities and colleges
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 10/2016, Volume 56, Issue 3, pp. 727 - 742
Hilbert space frames generalize orthonormal bases to allow redundancy in representations of vectors while keeping good reconstruction properties. A frame comes... 
Polytopes | Hilbert space frames | Computational Mathematics and Numerical Analysis | Convex geometry | 52B05 | Mathematics | Combinatorics | 42C15 | MATHEMATICS | COMPUTER SCIENCE, THEORY & METHODS | SPECTRUM | Algorithms | Frames | Operators | Mathematical analysis | Inequalities | Norms | Representations
Journal Article
Results in Mathematics, ISSN 1422-6383, 6/2013, Volume 63, Issue 3, pp. 1243 - 1255
K-frames were recently introduced by Găvruţa in Hilbert spaces to study atomic systems with respect to a bounded linear operator. From her discussions there... 
ordinary frame | Bessel sequence | Mathematics, general | K -frame | Mathematics | 42C15 | K-frame | MATHEMATICS | MATHEMATICS, APPLIED | BANACH-SPACES | OPERATORS | Computer science | Analysis
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 3/2018, Volume 211, Issue 3, pp. 1119 - 1148
We study nonuniform sampling in shift-invariant spaces and the construction of Gabor frames with respect to the class of totally positive functions whose... 
Mathematics, general | Mathematics | 42C40 | 42C15 | 94A20 | INTERPOLATION | MATHEMATICS | LOCALIZATION | DENSITY THEOREMS | RIESZ BASES | MATRICES | BARGMANN-FOCK SPACE | TRANSFORM | BANACH FRAMES | Frames | Theorems | Fourier transforms | Entire functions | Metric space | Sampling | Density | Invariants
Journal Article
Advances in Pure and Applied Mathematics, ISSN 1867-1152, 11/2014, Volume 5, Issue 4, pp. 243 - 253
The goal is to construct random frames and study properties of such frames. Starting with the construction of unimodular random sequences whose expected... 
random matrix | frames | Autocorrelation | sequences | 94A12 | 42C15 | Frames | Sequences | Random matrix
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 04/2013, Volume 162, Issue 6, pp. 1003 - 1031
Let g be a totally positive function of finite type, that is, (g) over cap(xi) =Pi(M)(nu=1)(1+2 pi i delta(nu)xi)(-1) for delta(nu) is an element of R,... 
DENSITY | INTERPOLATION | MATHEMATICS | TIME-FREQUENCY ANALYSIS | DECAY | RECONSTRUCTION | THEOREMS | SHIFT-INVARIANT SPACES | REPRESENTATION | TRANSFORM | WEYL-HEISENBERG FRAMES | Mathematics - Functional Analysis | 42C40 | 42C15 | 94A20
Journal Article
Constructive Approximation, ISSN 0176-4276, 12/2019, Volume 50, Issue 3, pp. 507 - 542
In analog-to-digital conversion, signal decimation has been proven to greatly improve the efficiency of data storage while maintaining high accuracy. When one... 
Sigma-Delta quantization | Numerical Analysis | Analysis | Mathematics | Unitarily generated frames | 42C15 | Decimation
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 2017, Volume 2017, Issue 1
Optimal asymptotic orders of the probabilistic linear \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}... 
28C20 | 41A46 | 41A25 | Gaussian measure | probabilistic linear widths | weighted Sobolev classes | Research | Jacobi weights | 42C15
Journal Article
Banach Journal of Mathematical Analysis, ISSN 1735-8787, 2015, Volume 9, Issue 1, pp. 1 - 16
A definition of frames in Krein spaces is stated and a complete characterization is given by comparing them to frames in the associated Hilbert space. The... 
Frames | Unbounded gram operator | W-metric | Krein spaces | MATHEMATICS | MATHEMATICS, APPLIED | unbounded Gram operator
Journal Article
Bulletin of the Iranian Mathematical Society, ISSN 1017-060X, 8/2019, Volume 45, Issue 4, pp. 1091 - 1104
In this paper, we intend to introduce the concept of c-K-g-frames, which are the generalization of K-g-frames. In addition, we prove some new results on... 
c-K-g-frame | 42C40 | Mathematics, general | Mathematics | K-g-frame | K-frame | g-Frame | 42C15 | MATHEMATICS | STABILITY
Journal Article
Monatshefte für Mathematik, ISSN 0026-9255, 12/2011, Volume 164, Issue 4, pp. 393 - 426
In recent years directional multiscale transformations like the curvelet- or shearlet transformation have gained considerable attention. The reason for this is... 
Wavefront set | Continuous frames | Secondary 42C40 | Microlocal analysis | Shearlets | Mathematics, general | Mathematics | Primary 42C15 | MATHEMATICS | Anisotropy | Analysis
Journal Article
Journal of Inequalities and Applications, ISSN 1029-242X, 12/2019, Volume 2019, Issue 1, pp. 1 - 17
To construct dual frames with good structure for a given frame is a fundamental problem in the theory of frames. The tensor product duals of tensor product... 
47A80 | Dual frame | Frame | 41A58 | Analysis | Tensor product frame | Mathematics, general | Mathematics | Applications of Mathematics | 42C15 | MATHEMATICS | MATHEMATICS, APPLIED | Frames | Tensors | Hilbert space | Mathematical analysis
Journal Article
Complex Analysis and Operator Theory, ISSN 1661-8254, 10/2019, Volume 13, Issue 7, pp. 2993 - 3021
In this article, we first induce an action of a topological group $${\mathbb {G}}$$ G on $$\ell ^2({\mathbb {Z}}_N^d)$$ ℓ 2 ( Z N d ) from a given action of... 
Framelet | Dual framelet | Dual Gramian | Operator Theory | Group action | Wavelet system | 42C40 | Analysis | Frame operator | Mathematics, general | Mathematics | 42C15
Journal Article
Applied and Computational Harmonic Analysis, ISSN 1063-5203, 05/2019, Volume 46, Issue 3, pp. 544 - 568
Equiangular tight frames (ETFs) and biangular tight frames (BTFs) – sets of unit vectors with basis-like properties whose pairwise absolute inner products... 
Biangular tight frames | Difference sets | Partial difference sets | Equiangular tight frames | Harmonic frames | Relative difference sets | Grassmannian line packings | Divisible difference sets | 05B10 | 42C15 | EXISTENCE | MATHEMATICS, APPLIED | PARAMETERS | LINES | BOUNDS | MATRICES | CONSTRUCTION | Exchange-traded funds | Analysis | Mathematics - Functional Analysis
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 03/2018, Volume 291, Issue 4, pp. 669 - 681
We study the minimizers of the fusion frame potential in the case that both the weights and the dimensions of the subspaces are fixed and not necessarily... 
Primary: 42C15; Secondary: 42C99 | Frames | tight fusion frames | 42C40 | fundamental inequality | irregularity | fusion frames | fusion frame potential | 15A60 | MATHEMATICS
Journal Article
Bulletin of the Iranian Mathematical Society, ISSN 1017-060X, 4/2019, Volume 45, Issue 2, pp. 377 - 399
In this paper, we present an algorithm—gradient descent of the frame potential—for increasing the degree of tightness of any finite admissible frame, and show... 
Frame | A-admissible | Frame potential | Secondary 42C40 | Tight frame | Mathematics, general | Mathematics | Primary 42C15 | MATHEMATICS
Journal Article
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