Related papers: Symmetric function kernels and sweeping of measure…
The purpose of this article is to introduce a new class of kernels on SO(3) for approximation and interpolation, and to estimate the approximation power of the associated spaces. The kernels we consider arise as linear combinations of…
This is an expository paper on approximating functions from general Hilbert or Banach spaces in the worst case, average case and randomized settings with error measured in the $L_p$ sense. We define the power function as the ratio between…
Concepts from information geometry are used to analyse parameter sensitivity for a nuclear energy density functional, representative of a class of semi-empirical functionals that start from a microscopically motivated ansatz for the density…
We reprove the well known fact that the energy distance defines a metric on the space of Borel probability measures on a Hilbert space with finite first moment by a new approach, by analyzing the behavior of the Gaussian kernel on Hilbert…
The estimation of potential fields such as the gravitational or magnetic potential at the surface of a spherical planet from noisy observations taken at an altitude over an incomplete portion of the globe is a classic example of an…
Motivated by applications to the study of stochastic processes, we introduce a new analysis of positive definite kernels $K$, their reproducing kernel Hilbert spaces (RKHS), and an associated family of feature spaces that may be chosen in…
Statistical depth is the act of gauging how representative a point is compared to a reference probability measure. The depth allows introducing rankings and orderings to data living in multivariate, or function spaces. Though widely applied…
We investigate a potential obtained as the convolution of a radially symmetric function and the characteristic function of a body (the closure of a bonded open set) with exterior cones. In order to restrict the location of a maximizer of…
Considering quantum cosmological minisuperspace models with positive potential, we present evidence that (i) despite common belief there are perspectives for defining a unique, naturally preferred decomposition of the space H of wave…
This article establishes sharp inverse and saturation statements for kernel-based approximation using finitely smooth Sobolev kernels on bounded Lipschitz regions. The analysis focuses on the superconvergence regime, for which direct…
The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…
Satellites mapping the spatial variations of the gravitational or magnetic fields of the Earth or other planets ideally fly on polar orbits, uniformly covering the entire globe. Thus, potential fields on the sphere are usually expressed in…
The self-energy screening correction is evaluated in a model in which the effect of the screening electron is represented as a first-order perturbation of the self energy by an effective potential. The effective potential is the Coulomb…
We prove general results about separation and weak$^\#$-convergence of boundedly finite measures on separable metric spaces and Souslin spaces. More precisely, we consider an algebra of bounded real-valued, or more generally a $*$-algebra…
In a filtered measure space, a characterization of weights for which the trace inequality of a positive operator holds is given by the use of discrete Wolff's potential. A refinement of the Carleson embedding theorem is also introduced.…
Various convergence results for the Bergman kernel of the Hilbert space of all polynomials in \C^{n} of total degree at most k, equipped with a weighted norm, are obtained. The weight function is assumed to be C^{1,1}, i.e. it is…
This paper presents a constructive proof of the existence of a regular non-atomic strictly-positive measure on any second-countable non-atomic locally compact Hausdorff space. This construction involves a sequence of finitely-additive set…
We study power boundedness and related properties such as mean ergodicity for (weighted) composition operators on function spaces defined by local properties. As a main application of our general approach we characterize when (weighted)…
The new scheme of the energy measurement of the extremely high energy electron beam with the inverse Compton scattering between electrons and microwave photons requires the precise calculation of the interaction cross section of electrons…
This paper is devoted to establishing the kernel theorems for $\alpha$-modulation spaces in terms of boundedness and compactness. We characterize the boundedness of a linear operator $A$ from an $\alpha$-modulation space…