Related papers: A weight function theory of positive order basis f…
I develop a weight func theory of zero order basis func interpolants and smoothers.**Ch1 Basis funcs and data spaces are defined using wt funcs. Data (native)spaces are used to formulate the variational problems which define our…
This document is a brief overview of two documents which continue to develop the weight function theory of basis function smoothers and interpolants. One document considers the zero order theory and one considers the positive order theory.
We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the…
We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…
In this paper a new class of radial basis functions based on hyperbolic trigonometric functions will be introduced and studied. We focus on the properties of their generalised Fourier transforms with asymptotics. Therefore we will compute…
This work characterizes the structure of third and forth order WENO weights by deducing data bounded condition on third order polynomial approximations. Using these conditions, non-linear weights are defined for third and fourth order data…
Soft extrapolation refers to the problem of recovering a function from its samples, multiplied by a fast-decaying window and perturbed by an additive noise, over an interval which is potentially larger than the essential support of the…
The main aim of this work is not to improve any existing non-linear weight but to give a generalized framework for the construction of non-linear weights to get non-oscillatory third order WENO schemes. It is done by imposing necessary…
This paper introduces a new functional expansion framework that extends classical ideas beyond the Taylor series. Unlike traditional Taylor expansions based on local polynomial approximations, the proposed approach arises from exact…
We solve an interpolation problem in $A^p_\alpha$ involving specifying a set of (possibly not distinct) $n$ points, where the $k^{\textrm{th}}$ derivative at the $k^{\textrm{th}}$ point is up to a constant as large as possible for functions…
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 consider the approximation of functions by radial basis function interpolants. There is a plethora of results about the asymptotic behaviour of the error between appropriately smooth functions and their interpolants, as the…
We perform conformal perturbation theory by marginal operators to first order. A suitable renormalization method is needed that makes the conformal invariance of the deformed correlation functions manifest. Combining the embedding space…
For Paley-Wiener functions on weighted combinatorial finite or infinite graphs we develop a weighted sampling theory in which samples are defined as inner products with weight functions (measuring devices). Three reconstruction methods are…
In the first part, we concentrate on CFTs in coordinate space. We lay the foundations of Conformal Field Theory and we also demonstrate a method where by using the embedding formalism we can derive up to n-point scalar conformal…
We study multivariate integration and approximation for functions belonging to a weighted reproducing kernel Hilbert space based on half-period cosine functions in the worst-case setting. The weights in the norm of the function space depend…
The present paper is intended to provide the basis for the study of weakly differentiable functions on rectifiable varifolds with locally bounded first variation. The concept proposed here is defined by means of integration by parts…
The error between appropriately smooth functions and their radial basis function interpolants, as the interpolation points fill out a bounded domain in R^d, is a well studied artifact. In all of these cases, the analysis takes place in a…
Submodular set functions are undoubtedly among the most important building blocks of combinatorial optimization. Somewhat surprisingly, continuous counterparts of such functions have also appeared in an analytic line of research where they…
Given a positive weight function and an isometry map on a Hilbert spaces $\mathcal{H}$, we study a class of linear maps which is a $g$-frame, $g$-Riesz basis and a $g$-orthonormal basis for $\mathcal{H}$ with respect to $\mathbb{C}$ in…