Related papers: Coercivity estimates for integro-differential oper…
In this article, we propose new proportional fractional operators generated from local proportional derivatives of a function with respect to another function. We present some properties of these fractional operators which can be also…
An analytically derived 'integral operator' approach is introduced to estimate the expectation value of a quantum operator for an evolving state weighted with an exponential function. This allows to compute quantities useful in Nuclear…
We obtain two-sided estimates for the heat kernel (or the fundamental function) associated with the following fractional Schr\"odinger operator with negative Hardy potential $$\Delta^{\alpha/2} -\lambda |x|^{-\alpha}$$ on $\RR^d$, where…
The purpose of this article is to study pseudospectral properties of the one-dimensional Schr\"{o}dinger operator perturbed by a complex steplike potential. By constructing the resolvent kernel, we show that the pseudospectrum of this…
The work is dedicated to the construction of the Cauchy-Szeg\"o kernel for the Cauchy-Szeg\"o projection integral operator from the space of $L^2$-integrable functions defined on the boundary of the quaternionic Siegel upper half space to…
The Carleman operator is defined as integral operator with kernel $(t+s)^{-1}$ in the space $L^2 ({\Bbb R}_{+}) $. This is the simplest example of a Hankel operator which can be explicitly diagonalized. Here we study a class of self-adjoint…
In this note, we prove lower and upper bounds for Dirac operators of submanifolds in certain ambient manifolds in terms of conformal and extrinsic quantities.
In this paper we establish optimal regularity estimates and smoothness of free boundaries for nonlocal obstacle problems governed by a very general class of integro-differential operators with possibly singular kernels. More precisely, in…
The solution of a partial differential equation can be obtained by computing the inverse operator map between the input and the solution space. Towards this end, we introduce a \textit{multiwavelet-based neural operator learning scheme}…
We address the estimation of "extreme" conditional quantiles i.e. when their order converges to one as the sample size increases. Conditions on the rate of convergence of their order to one are provided to obtain asymptotically Gaussian…
For a class of one-dimensional determinantal point processes including those induced by orthogonal projections with integrable kernels satisfying a growth condition, it is proved that their conditional measures, with respect to the…
Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…
A necessary condition and a sufficient condition for one weight norm inequalities on Morrey spaces to hold are given for the fractional maximal operator and the fractional integral operator. We clarify the difference between the behavior of…
For doubling weights, we obtain a necessary and sufficient condition such that the one weighted inequality of the integral operator induced by Hardy kernels on the unit disk holds. This confirms a conjecture by Guo and Wang in such…
We study linear integro-differential equations in Hilbert spaces with operator-valued kernels and give sufficient conditions for the well-posedness. We show that several types of integro-differential equations are covered by the class of…
In this paper, we study a class of multilinear fractional integral operators which have correlation kernels $\prod_{1\leq i<j \leq k}|x_i-x_j|^{-\alpha_{ij}}$. The necessary and sufficient conditions are obtained under which these oprators…
In this paper, we have introduced the Prabhakar fractional $q$-integral and $q$-differential operators. We first study the semi-group property of the Prabhakar fractional $q$-integral operator, which allowed us to introduce the…
The aim of these notes is to describe some recent results concerning dispersive estimates for principally normal pseudodifferential operators. The main motivation for this comes from unique continuation problems. Such estimates can be used…
This is the second part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. We consider a substitute to the notion of pointwise bounds for kernels of operators which usually is a…
We characterize those homogeneous translation invariant symmetric non-local operators with positive maximum principle whose harmonic functions satisfy Harnack's inequality. We also estimate the corresponding semigroup and the potential…