Related papers: Inverting weak random operators

Weak measurements are a new tool for characterizing post-selected quantum systems during their evolution. Weak measurement was originally formulated in terms of von Neumann interactions which are practically available for only the simplest…

Usually such area of mathematics as differential equations acts as a consumer of results given by functional analysis. This article will give an example of the reverse interaction of these two fields of knowledge. Namely, the derivation and…

In this paper, we investigate the behavior of the bounds of the composition for rough singular integral operators on the weighted space. More precisely, we obtain the quantitative weighted bounds of the composite operator for two singular…

We consider the weak to strong type problem for two weight norm inequalities for Calder\'on-Zygmund operators with doubling weights. We show that if a Calder\'on-Zygmund operator T is weak type (2,2) with doubling weights, then it is strong…

The paper deals with nonlocal differential operators possessing a term with frozen (fixed) argument appearing, in particular, in modelling various physical systems with feedback. The presence of a feedback means that the external affect on…

We consider an inverse problem for a higher order elliptic operator where the principal part is the polyharmonic operator $(-\Delta)^m$ with $ m \geq 2$. We show that the map from the coefficients to a certain bilinear form is injective. We…

Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…

Let $0\leq \alpha<n$, $m\in \mathbb{N}$ and let consider $T_{\alpha,m}$ be a of integral operator, given by kernel of the form $$K(x,y)=k_1(x-A_1y)k_2(x-A_2y)\dots k_m(x-A_my),$$ where $A_i$ are invertible matrices and each $k_i$ satisfies…

Consider an invertible measure-preserving transformation of a probability space. A finite partition of the space is called weakly independent if there are infinitely many images of this partition under powers of the transformation that are…

In this work, we establish the asymptotic normality of the deconvolution kernel density estimator in the context of strongly mixing random fields. Only minimal conditions on the bandwidth parameter are required and a simple criterion on the…

Four possible definitions of the commutation relation $[S,T]=\Id$ of two closable unbounded operators $S,T$ are compared. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space $\H$ where the…

Inverse spectral problems for Sturm-Liouville operators with nonlocal boundary conditions are studied. As the main spectral characteristics we introduce the so-called Weyl-type function and two spectra, which are generalizations of the…

We give alternative proofs to certain results in the paper "Weak limits of almost invariant projections" by using ultraproducts of operators.

The paper proves two results involving a pair (A,B) of P-biisometric or (m,P)-biisometric Hilbert-space operators for arbitrary positive integer m and positive operator P. It is shown that if A and B are power bounded and the pair (A,B) is…

This paper investigates the problem of estimating the spectral power parameters of random analog sources using numerical measurements acquired with minimum digitization complexity. Therefore, spectral analysis has to be performed with…

We give a characterization of the invariant measures for the exclusion process on the integers with certain reversible transition kernels. Some examples include all nearest-neighbor kernels with asymptotic mean zero. One tool used is a…

This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…

In different branches of physics, we frequently deal with vector del operator ($\vec{\nabla}$). This del operator is generally used to find curl or divergence of a vector function or gradient of a scalar function. In many important cases,…

This paper proposes a new and efficient numerical algorithm for recovering the damping coefficient from the spectrum of a damped wave operator, which is a classical Borg-Levinson inverse spectral problem. The algorithm is based on inverting…

We consider the small-angle multiple neutron scattering and a possibility of its model-free analysis by the inverse problem method. We show that the ill-defined problem is essentially regularized by use of a planar detector without a…