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Denote by $T_n^d(A)$ an upper triangular operator matrix of dimension $n$ whose diagonal entries are given and the others are unknown. In this article we provide necessary and sufficient conditions for various types of Fredholm and Weyl…
In this paper, we explore the relationship between the operators mapping atoms to molecules in local Hardy spaces $h^p(\mathbb{R}^n)$ and the size conditions of its kernel. In particular, we show that if the kernel of a…
Local Convertibility refers to the possibility of transforming a given state into a target one, just by means of LOCC with respect to a given bipartition of the system and it is possible if and only if all the Renyi-entropies of the initial…
The asymptotic properties of integral operators with the generalized sine kernel acting on the real axis are studied. The formulas for the resolvent and the Fredholm determinant are obtained in the large x limit. Some applications of the…
In this paper, we are mainly concerned with studying arbitrary unbounded square roots of linear operators as well as some of their basic properties. The paper contains many examples and counterexamples. As an illustration, we give explicit…
Convolutional neural networks perform a local and translationally-invariant treatment of the data: quantifying which of these two aspects is central to their success remains a challenge. We study this problem within a teacher-student…
This paper is concerned with the question of reconstructing a vector in a finite-dimensional real Hilbert space when only the magnitudes of the coefficients of the vector under a redundant linear map are known. We analyze various Lipschitz…
In many tasks, in particular in natural science, the goal is to determine hidden system parameters from a set of measurements. Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse…
New index transforms, involving the square of Bessel functions of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue spaces.…
We define a set of operators that localise a radial image in radial space and radial frequency simultaneously. We find the eigenfunctions of this operator and thus define a non-separable orthogonal set of radial wavelet functions that may…
In the article we study properties of the random integral operator in $L_2(\mathbb{R})$ whose kernel is obtained as a convolution of Gaussian density with a stationary point process.
Multiscale transforms for real-valued data, based on interpolatory subdivision operators have been studied in recent year. They are easy to define, and can be extended to other types of data, for example to manifold-valued data. In this…
Robot localization is an inverse problem of finding a robot's pose using a map and sensor measurements. In recent years, Invertible Neural Networks (INNs) have successfully solved ambiguous inverse problems in various fields. This paper…
M. Embry and A. Lambert initiated the study of a semigroup of operators $\{S_t\}$ indexed by a non-negative real number $t$ and termed it as weighted translation semigroup. The operators $S_t$ are defined on $L^2(\mathbb R_+)$ by using a…
In this article we consider direct and inverse problems for $\alpha$-stable, elliptic nonlocal operators whose kernels are possibly only supported on cones and which satisfy the structural condition of \emph{directional antilocality} as…
In this paper we consider a large class of fully nonlinear integro-differential equations. The class of our nonlocal operators we consider is not spatial homogeneous and we put mild assumptions on its kernel near zero. We prove the H\"older…
A method of approximating the inverse Radon transform on the plane by integrating against a smooth kernel is investigated. For piecewise smooth integrable functions, convergence theorems are proven and Gibbs phenomena are ruled out.…
We extend the recent results concerning boundedness of the maximal regularity operator on tent spaces. This leads us to develop a singular integral operator theory on tent spaces. Such operators have operator-valued kernels. A seemingly…
In the context of inverse reinforcement learning (IRL) with a single expert, adversarial inverse reinforcement learning (AIRL) serves as a foundational approach to providing comprehensive and transferable task descriptions. However, AIRL…
Our main result is a theorem saying that a bounded operator $A$ on a Hilbert space belongs to a certain set associated with its self-commutator $[A^*,A]$, provided that $A-zI$ can be approximated by invertible operators for all complex…