相关论文: Interpolation by positive harmonic functions
Based on the sampling theorem, interpolation should be conducted by employing the sinc functions as the kernels. Inspired by the fact that the discrete Fourier transform (DFT) is sampled from the discrete time Fourier transform, a fast…
The Hermite-Birkhoff interpolation problem of a function given on arbitrarily distributed points on the sphere and other manifolds is considered. Each proposed interpolant is expressed as a linear combination of basis functions, the…
In this paper, we investigate the problem of designing compact support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an infinite nonlinear problem to a finite…
The aim of this short note is to show how can be derived from the properties of fundamental interpolation polynomials some nice identities.
For the classic aesthetic interpolation problem, we propose an entirely new thought: apply the golden section. For how to apply the golden section to interpolation methods, we present three examples: the golden step interpolation, the…
Blending schemes based on circles provide smooth `fair' interpolations between series of points. Here we demonstrate a simple, robust set of algorithms for performing circle blends for a range of cases. An arbitrary level of G-continuity…
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 introduced positive cones in an earlier paper as a notion of ordering on central simple algebras with involution that corresponds to signatures of hermitian forms. In the current paper we describe signatures of hermitian forms directly…
We consider cones in a Hilbert space associated to two von Neumann algebras and determine when one algebra is included in the other. If a cone is assocated to a von Neumann algebra, the Jordan structure is naturally recovered from it and we…
There exist efficient algorithms to project a point onto the intersection of a convex cone and an affine subspace. Those conic projections are in turn the work-horse of a range of algorithms in conic optimization, having a variety of…
The generation of harmonics by atoms interacting with two circularly polarized and frequency related laser fields is addressed through ab initio numerical simulations. A detailed charaterization of a few specific harmonics is given. In…
The problem of interpolation at $(n+1)^2$ points on the unit sphere $\mathbb{S}^2$ by spherical polynomials of degree at most $n$ is proved to have a unique solution for several sets of points. The points are located on a number of circles…
The mean flux theorems are proved for solutions of the Helmholtz equation and its modified version. Also, their converses are considered along with some other properties which generalise those that guarantee harmonicity.
This note presents a simple approach to proving the interlacing properties of positive zeros of Bessel functions of the first kind. The approach relies only on the standard recurrence relations between Bessel functions and characterising…
This paper gives a definition of g-harmonic functions and shows the relation between the g-harmonic functions and g-martingales. It's direct to construct such relation under smooth case, but for continuous case we need the theory of…
Given an interpolating Blaschke product $B$ with zeros $\{a_j\}$, we seek to characterize the sequences of values $\{w_j\}$ for which the interpolation problem $$f(a_j)=w_j\qquad (j=1,2,\dots)$$ can be solved with a function $f$ from the…
A closed convex polytope in n dimensions defined by m linear inequality constraints is considered. If L is a straight line drawn in any direction from any feasible point P, then in general, it intersects every constraint at one point,…
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…
Indecomposible semifinite harmonic functions on the direct product of graded graphs are classified. As a particular case, the full list of indecomposible traces for the infinite inverse symmetric semigroup is obtained.
Polynomial optimization encompasses a broad class of problems in which both the objective function and constraints are polynomial functions of the decision variables. In recent years, a substantial body of research has focused on…