相关论文: Dirichlet integral dual-access collocation-kernel …
This article gives a ``fundamental solution'' based energy-norm harmonic interpolation approach for two half-space settings of interest: the upper-half $\mathbb{R}^n$ plane, where fundamental solutions satisfy Laplace's equation, and the…
In this paper we study two separate problems on interpolation. We first give some new equivalences of Stout's Theorem on necessary and sufficient conditions for a sequence of points to be an interpolating sequence on a finite open Riemann…
We introduce and systematically develop two classes of discrete integrable operators: those with $2\times 2$ matrix kernels and those possessing general differential kernels, thereby generalizing the discrete analogue previously studied. A…
In this paper we present an efficient algorithm for bivariate interpolation, which is based on the use of the partition of unity method for constructing a global interpolant. It is obtained by combining local radial basis function…
This paper presents a general high-order kernel regularization technique applicable to all four integral operators of Calder\'on calculus associated with linear elliptic PDEs in two and three spatial dimensions. Like previous density…
This note is about promoting singularity subtraction as a helpful tool in the discretization of singular integral operators on curved surfaces. Singular and nearly singular kernels are expanded in series whose terms are integrated on…
We formulate the Bergman-type interpolation problem on finite open Riemann surfaces covered by the unit disk. Our version of the interpolation problem generalizes Bergman-type interpolation problems previously studied by Seip, Berntsson,…
We provide a new approach for computing integrals over hypersurfaces in the level set framework. The method is based on the discretization (via simple Riemann sums) of the classical formulation used in the level set framework, with the…
Asymptotic expansions as well as necessary and sufficient conditions are provided for the pointwise convergence of the spherical partial integrals of the associated Fourier transforms on the real hyperbolic space. The proposed method…
Identifying and suppressing streaking artifacts is one of the most challenging problems in quantitative susceptibility mapping. The measured phase from tissue magnetization is assumed to be the convolution by the magnetic dipole kernel;…
We investigate the Pick problem for the polydisk and unit ball using dual algebra techniques. Some factorization results for Bergman spaces are used to describe a Pick theorem for any bounded region in $\mathbb{C}^d$.
A general interpolation problem with operator argument is studied for functions f from the de Branges-Rovnyak space H(s) associated with an analytic function s mapping the open unit disk D into the closed unit disk. The interpolation…
This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…
We revisit the classical kernel method of approximation/interpolation theory in a very specific context motivated by the desire to obtain a robust procedure to approximate discrete data sets by (super)level sets of functions that are merely…
We formalize a technique for embedding Riemann sufraces properly into \C^2, and we generalize all known embedding results to allow interpolation on prescribed discrete sequences.
We consider piecewise linear interpolation from the perspective of kernel interpolation and quadrature. If the Sobolev space $W_2^1(0, 1)$ is equipped with a suitable inner product, its reproducing kernel is piecewise linear and gives rise…
We present a unified interpolation scheme that combines compactly-supported positive-definite kernels and multivariate polynomials. This unified framework generalizes interpolation with compactly-supported kernels and also classical…
Compact analytical forms are derived for the interactions involving thin disks in two dimensions using an integration approach. These include interactions between a disk and a material point, between two disks, and between a disk and a…
We present an analytic method to minimize the magnetic cross-talk in twin-aperture cos-theta dipoles. In the single-aperture cos-theta layout, the coil design can be performed with an analytic approach, based on a sector coil approximation.…
Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces $\mathcal{D}_\alpha$. Specifically we study differences of composition operators on the Dirichlet space $\mathcal{D}$ and $S^2$,…