相关论文: Lineability and uniformly dominated sets of summin…

We consider a symmetrical star-shaped network, in which bandwidth is shared among the active connections according to the "min" policy. Starting from a chaos propagation hypothesis, valid when the system is large enough, one can write…

Linear harmonic number sums had been studied by a variety of authors during the last centuries, but only few results are known about nonlinear Euler sums of quadratic or even higher degree. The first systematic study on nonlinear Euler sums…

This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…

Linear harmonic number sums had been studied by a variety of authors during the last centuries, but only few results are known about nonlinear Euler sums of quadratic or even higher degree. The first systematic study on nonlinear Euler sums…

Quantitative stochastic homogenization of linear elliptic operators is by now well-understood. In this contribution we move forward to the nonlinear setting of monotone operators with $p$-growth. This work is dedicated to a quantitative…

In this paper we introduce a very general setting dealing with the superposition of operators of any positive order and provide a systematic study of them. We also provide examples and counterexamples, as well as characterizing properties…

We consider the problem of directly optimizing a non-linear function of an outcome, where this outcome itself is the sum of many small contributions. The non-linearity of the function means that the problem is not equivalent to the…

On the basis of the explicit formulae for the action of the unitary group of exponentials corresponding to almost solvable extensions of a given closed symmetric operator with equal deficiency indices, we derive a new representation for the…

A sum-dominant set is a finite set $A$ of integers such that $|A+A| > |A-A|$. As a typical pair of elements contributes one sum and two differences, we expect sum-dominant sets to be rare in some sense. In 2006, however, Martin and O'Bryant…

For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met, the…

For a general one-sided nonautonomous dynamics defined by a sequence of linear operators, we consider the notion of a polynomial dichotomy with respect to a sequence of norms and we characterize it completely in terms of the admissibility…

The difficulty for solving ill-posed linear operator equations in Hilbert space is reflected by the strength of ill-posedness of the governing operator, and the inherent solution smoothness. In this study we focus on the ill-posedness of…

The notion of uniform equicontinuity in measure at zero for sequences of additive maps from a normed space into the space of measurable operators associated with a semifinite von Neumann algebra is discussed. It is shown that uniform…

This paper is a contribution to the theory of dynamical sampling. Our purpose is twofold. We first consider representations of sequences in a Hilbert space in terms of iterated actions of a bounded linear operator. This generalizes recent…

In this paper, we explore the concept of multilinear operators that are multiple almost summing and present a new concept of type and cotype of multilinear operators and investigate the conditions for this new concept to recover the…

Strongly irreducible operators can be considered as building blocks for bounded linear operators on complex separable Hilbert spaces. Many bounded linear operators can be written as direct sums of at most countably many strongly irreducible…

We give a generalization of the Jordan canonical form theorem for a class of bounded linear operators on complex separable Hilbert spaces in terms of direct integrals. Precisely, we study the uniqueness of strongly irreducible…

In this paper we study shorted operators relative to two different subspaces, for bounded operators on infinite dimensional Hilbert spaces. We define two notions of complementability in the sense of Ando for operators, and study the…

We prove an uniform boundedness principle for the Lipschitz seminorm of continuous, monotone, positively homogeneous and subadditive mappings on suitable cones of functions. The result is applicable to several classes of classically…

We study the minus order on the algebra of bounded linear operators on a Hilbert space. By giving a characterization in terms of range additivity, we show that the intrinsic nature of the minus order is algebraic. Applications to…