Related papers: Classification of General Sequences by Frame-Relat…
A family of random matrices is said to converge strongly to a limiting family of operators if the operator norm of every noncommutative polynomial of the matrices converges to that of the limiting operators. Recent developments surrounding…
The concept of sequency holds a fundamental significance in signal analysis using Walsh basis functions. In this study, we closely examine the concept of sequency and explore the properties of sequency-complete and sequency-ordered…
In approximation theory classical discrete operators, like generalized sampling, Sz\'{a}sz-Mirak'jan, Baskakov and Bernstein operators, have been extensively studied for scalar functions. In this paper, we look at the approximation of…
Certain linear matrix operators arise naturally in systems analysis and design problems involving cascade interconnections of linear time-invariant systems, including problems of stabilization, estimation, and model order reduction. We…
We introduce real vector spaces composed of set-valued maps on an open set. They are also complete metric spaces, lattices, commutative rings. The set of differentiable functions is a dense subset of these spaces and the classical gradient…
We extend the theory of operator-valued frames (resp. bases), hence the theory of frames (resp. bases), for Hilbert spaces and Hilbert C*-modules, in two folds. This extension leads us to develop the theory of operator-valued frames (resp.…
Regular sequences are natural generalisations of fixed points of constant-length substitutions on finite alphabets, that is, of automatic sequences. Using the harmonic analysis of measures associated with substitutions as motivation, we…
The survey is devoted to diverse applications of Besov classes in operator theory. It is illustrated how Besov classes are used to describe Hankel operators of Schatten--von Neumann classes; various applications of this description are…
Unifying several directions of the development of the study of summing multilinear operators between Banach spaces, we construct a general framework that studies, under one single definition, multilinear operators that are summing with…
This paper introduces the class of grey-scale image stack operators as those that (a) map binary-images into binary-images and (b) commute on average with cross-sectioning. Equivalently, stack operators are 1-Lipchitz extensions of set…
Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective…
After an historical introduction on the standard algebraic approach to quantum mechanics of large systems we review the basic mathematical aspects of the algebras of unbounded operators. After that we discuss in some details their relevance…
The notion of the genus of a quadratic form is generalized to vertex operator algebras. We define it as the modular braided tensor category associated to a suitable vertex operator algebra together with the central charge. Statements…
Hilbert space frames generalize orthonormal bases to allow redundancy in representations of vectors while keeping good reconstruction properties. A frame comes with an associated frame operator encoding essential properties of the frame. We…
We introduce new techniques allowing one to construct diagonals of bounded Hilbert space operators and operator tuples under "Blaschke-type" assumptions. This provides a new framework for a number of results in the literature and…
The aim of this work is to study frame theory in quaternionic Hilbert spaces. We provide a characterization of frames in these spaces through the associated operators. Additionally, we examine frames of the form $\{Lu_i\}_{i \in I}$, where…
We present a spectral analysis for matrix scaling and operator scaling. We prove that if the input matrix or operator has a spectral gap, then a natural gradient flow has linear convergence. This implies that a simple gradient descent…
Ordered sequences of univariate or multivariate regressions provide statistical models for analysing data from randomized, possibly sequential interventions, from cohort or multi-wave panel studies, but also from cross-sectional or…
For operators generated by a certain class of infinite band matrices with matrix elements we establish a characterization of the resolvent set in terms of polynomial solutions of the underlying higher order finite difference equations. This…
This paper studies frames in Hilbert spaces generated by the orbits of (in)-finitely many vectors under a single operator, presenting new results on multiplication operators and operators composed of Jordan blocks, which generalizes…