Related papers: Random fusion frames are nearly equiangular and ti…
A randomized subspace action algorithm is investigated for fusion frame signal recovery problems. It is noted that Kaczmarz bounds provide upper bounds on the algorithm's error moments. The main question of which probability distributions…
An equiangular tight frame (ETF) is a set of equal norm vectors in a Euclidean space whose coherence is as small as possible, equaling the Welch bound. Also known as Welch-bound-equality sequences, such frames arise in various applications,…
Hyperuniform many-particle distributions possess a local number variance that grows more slowly than the volume of an observation window, implying that the local density is effectively homogeneous beyond a few characteristic length scales.…
A new notion in frame theory has been introduced recently that called woven frames. %From the perspective of others, Woven and weaving frames are powerful tools for pre-processing signals and distributed data processing. The purpose of…
We imagine an experiment on an unknown quantum mechanical system in which the system is prepared in various ways and a range of measurements are performed. For each measurement M and preparation rho the experimenter can determine, given…
We consider the space of complete and separable metric spaces which are equipped with a probability measure. A notion of convergence is given based on the philosophy that a sequence of metric measure spaces converges if and only if all…
In a series of papers Tsirelson constructed from measure types of random sets and generalised random processes a new range of examples for continuous tensor product systems of Hilbert spaces introduced by Arveson for classifying…
This paper addresses the problem of approximating an unknown function from point evaluations. When obtaining these point evaluations is costly, minimising the required sample size becomes crucial, and it is unreasonable to reserve a…
Controlled frames which presented to improve the numerical output of iterative algorithms for inverting the frame operator, have been introduced by Balazs and et al. Also, these frames are used by Bogdanova and et al. for spherical…
We derive easily verifiable conditions which characterize when complex Seidel matrices containing cube roots of unity have exactly two eigenvalues. The existence of such matrices is equivalent to the existence of equiangular tight frames…
In representations using frames, oblique duality appears in situations where the analysis and the synthesis has to be done in different subspaces. In some cases, we cannot obtain an explicit expression for the oblique duals and in others…
It's known that if $d^2$ vectors from $d$-dimensional Hilbert space $H$ form a SIC-POVM (SIC for short) then tensor square of those vectors form an equiangular tight frame on the symmetric subspace of $H\otimes H$. We prove that for any SIC…
The most fundamental notion for Hilbert space frames is the sequence of frame coefficients for a vector x in the space. Yet, we know little about the distribution of these coefficient sequences. In this paper, we make the first detailed…
We propose a new probabilistic characterization of the uniform distribution on the hypersphere in terms of the distribution of pairwise inner products, extending the ideas of \citep{cuesta2009projection,cuesta2007sharp} in a data-driven…
Almost-isometries are quasi-isometries with multiplicative constant one. Lifting a pair of metrics on a compact space gives quasi-isometric metrics on the universal cover. Under some additional hypotheses on the metrics, we show that there…
We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…
We provide sufficient conditions for quantitative convergence of the iterates of proximal splitting algorithms for minimizing a sum of functions on a metric space. The theory does not assume that the functions have common minima, nor does…
While the exact separability probability of 8/33 for two-qubit states under the Hilbert-Schmidt measure has been reported by Huong and Khoi [\href{https://doi.org/10.1088/1751-8121/ad8493}{J.Phys.A:Math.Theor.{\bf57}, 445304(2024)}],…
In this paper, we propose a stochastic forward-backward-forward splitting algorithm and prove its almost sure weak convergence in real separable Hilbert spaces. Applications to composite monotone inclusion and minimization problems are…
We investigate the intermediate permutational symmetries of a system of qubits, that lie in between the perfect symmetric and antisymmetric cases. We prove that, on average, pure states of qubits picked at random with respect to the uniform…