Related papers: Estimates for singular integrals and extrapolation
We show that the cone-adapted shearlet coefficients can be computed by means of the limited angle horizontal and vertical (affine) Radon transforms and the one-dimensional wavelet transform. This yields formulas that open new perspectives…
We obtain sampling and interpolation theorems in radial weighted spaces of analytic functions for weights of arbitrary (more rapid than polynomial) growth. We give an application to invariant subspaces of arbitrary index in large weighted…
In this paper we construct the fundamental solution to some integro-differential equation, as well as the intrinsic upper and lower estimates for this solution. As an application of constructed estimates we state a criterion when a given…
Explaining complex or seemingly simple machine learning models is an important practical problem. We want to explain individual predictions from a complex machine learning model by learning simple, interpretable explanations. Shapley values…
In this paper, we study the boundedness properties of the (dyadic) maximal bilinear operator associated with rough homogeneous kernels on $\mathbb{R}$. We establish sharp $L^{p_1}(\mathbb{R}) \times L^{p_2}(\mathbb{R}) \to…
For the general parametric regression models with covariates contaminated with normal measurement errors, this paper proposes an accelerated version of the classical simulation extrapolation algorithm to estimate the unknown parameters in…
This paper contains an $L^{p}$ improving result for convolution operators defined by singular measures associated to hypersurfaces on the motion group. This needs only mild geometric properties of the surfaces, and it extends earlier…
Recovering a function from integrals over conical surfaces recently got significant interest. It is relevant for emission tomography with Compton cameras and other imaging applications. In this paper, we consider the weighted conical Radon…
This paper presents new methodology for computationally efficient kernel density estimation. It is shown that a large class of kernels allows for exact evaluation of the density estimates using simple recursions. The same methodology can be…
The purpose of this announcement is to describe a development given in a series of forthcoming papers by the authors that concern operators of the form \[ f\mapsto \psi(x) \int f(\gamma_t(x)) K(t)\: dt, \] where $\gamma_t(x)=\gamma(t,x)$ is…
Applications of a simple thermal model to ultra-relativistic heavy-ion collisions are presented. We compute abundances of various hadrons, including particles with strange quarks, the pT-spectra, and the HBT radii for the pion. Surprising…
Interpolation is responsible for digital signal resampling and can significantly degrade the original signal quality if not done properly. For many years, optimal interpolation algorithms were sought within constrained classes of…
This paper explores possibilities for new uses of the Radon transform for imaging and analysis of lightfields. We show that the previously reported Dimansionality Gap can be derived from an ultrahyperbolic PDE, first proposed by F. John,…
We present a method to extrapolate nuclear binding energies from known values for neighbouring nuclei. We select four specific mass relations constructed to eliminate smooth variation of the binding energy as function nucleon numbers. The…
Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…
We show $L^p$ estimates for square roots of second order complex elliptic systems $L$ in divergence form on open sets in $\mathbb{R}^d$ subject to mixed boundary conditions. The underlying set is supposed to be locally uniform near the…
We study superpositions and direct integrals of quadratic and Dirichlet forms. We show that each quasi-regular Dirichlet space over a probability space admits a unique representation as a direct integral of irreducible Dirichlet spaces,…
Given a real-analytic function b(x) defined on a neighborhood of the origin with b(0) = 0, we consider local convolutions with kernels which are bounded by |b(x)|^(-a), where a > 0 is the smallest number for which |b(x)|^(-a) is not…
In recent years, many types of elliptical Radon transforms that integrate functions over various sets of ellipses/ellipsoids have been considered, relating to studies in bistatic synthetic aperture radar, ultrasound reflection tomography,…
In this paper, we derive a gradient estimate for the linear combinations of eigenforms of the Hodge Laplacian on a closed manifold. The estimate is given in terms of the dimension, volume, diameter and curvature bound of the manifold. As an…