Related papers: Inverting weak random operators
We find explicitly the Green kernel of a random Schr\"odinger operator with Brownian white noise. To do this, we first handle the random operator by defining it weakly using the inner product of a Hilbert space. Then, using classic…
We prove a weak-type estimate for a class of operators extending some of the almost orthogonality issues involved in the study of the bilinear Hilbert transform by Lacey and Thiele.
We present the weighted weak group inverse, which is a new generalized inverse of operators between two Hilbert spaces, introduced to extend weak group inverse for square matrices. Some characterizations and representations of the weighted…
We study the weak convergence of iterates of so-called centred kernel quadratic stochastic operators. These iterations, in a population evolution setting, describe the additive perturbation of the arithmetic mean of the traits of an…
Using simultaneously two operator identities, we consider the inversion of the convolution operators on a rectangular. The structure of the inverse operators and of some corresponding forms, which are important in signal processing, is…
Radial convolution operators on free groups with nonnegative kernel of weak type $(2,2)$ and of restricted weak type $(2,2)$ are characterized. Estimates of weak type $(p,p)$ are obtained as well for $1<p<2.$
The study of the phenomenon of quantum weak turbulence is extended by determining the quasiparticle spectrum associated with such a system using a Green's function approach. The quasiparticle spectrum calculated establishes the dissipative…
We study an inverse scattering problem associated with a Schr\"odinger system where both the potential and source terms are random and unknown. The well-posedness of the forward scattering problem is first established in a proper sense. We…
In this paper, we propose a weak regularity principle which is similar to both weak K\"onig's lemma and Ramsey's theorem. We begin by studying the computational strength of this principle in the context of reverse mathematics. We then…
By a reduction method, the limiting weak-type behaviors of factional maximal operators and fractional integrals are established without any smoothness assumption on the kernel, which essentially improve and extend previous results. As a…
This research was devoted to investigate the inverse spectral problem of Sturm-Liouville operator with many frozen arguments. Under some assumptions, the authors obtained uniqueness theorems. At the end, a numerical simulation for the…
We obtain weak type (1,1) estimates for the inverses of truncated discrete rough Hilbert transform. We include an ex- ample showing that our result is sharp. One of the ingredients of the proof are regularity estimates for convolution of…
In this paper, we introduce a weak group inverse (called the WG inverse in the present paper) for square matrices of an arbitrary index, and give some of its characterizations and properties. Furthermore, we introduce two orders: one is a…
This paper investigates an inverse random source problem for the stochastic fractional Helmholtz equation. The source is modeled as a centered, complex-valued, microlocally isotropic generalized Gaussian random field whose covariance and…
Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…
In this paper, we establish quantitative weak type estimates for operators that are dominated by (fractional) sparse operators in bilinear sense. Specifically, we derive bounds for both the restricted weak type $L^{p,1}\rightarrow…
We establish a uniform estimate for a bilinear fractional integral operator via restricted weak-type endpoint estimates and Marcinkiewicz interpolation. This estimate is crucial in the integrability analysis of a tensor-valued bilinear…
Inverse spectral problems are studied for first-order integro-differential operators on a finite interval. These problems consist in recovering some components of the kernel from one or multiple spectra. Uniqueness theorems are proved for…
We investigate algebraic properties of weakly commutative triples, appearing in the theory of integrable nonlinear partial differential equations. Algebraic technique of skew fields of formal pseudodifferential operators as well as skew Ore…
The analysis of the dependence of integral operators on perturbations plays an important role in the study of inverse problems and of perturbed boundary value problems. In this paper we focus on the mapping properties of the volume…