Related papers: Dual Basis Functions in Subspaces
We describe all metric spaces that have sufficently many affine functions. As an application we obtain a metric characterization of linear-convex subsets of Banach spaces.
We study a novel spline-like basis, which we name the "falling factorial basis", bearing many similarities to the classic truncated power basis. The advantage of the falling factorial basis is that it enables rapid, linear-time computations…
Finite geometry is employed to underpin operators in finite, d, dimensional Hilbert space. The central role of mutual unbiased bases (MUB) states projectors is exhibited. Interrelation among operators in Hilbert space, revealed through…
We associate a polynomial to any diagram of unit cells in the first quadrant of the plane using Kohnert's algorithm for moving cells down. In this way, for every weak composition one can choose a cell diagram with corresponding row-counts,…
Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate…
The general properties of two-dimensional generalized Bessel functions are discussed. Various asymptotic approximations are derived and applied to analyze the basic structure of the two-dimensional Bessel functions as well as their nodal…
We explore the convergence of Kergin interpolation polynomials of holomorphic functions in Banach spaces, which need not be of bounded type. We also investigate a case where the Kergin series diverges.
Let G be a finite abelian group. We examine the discrepancy between subspaces of l^2(G) which are diagonalized in the standard basis and subspaces which are diagonalized in the dual Fourier basis. The general principle is that a Fourier…
Functions with uniform sublevel sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used in multicriteria optimization, decision theory, mathematical…
We provide an algorithm for the construction of orthonormal multivariate polynomials that are symmetric with respect to the interchange of any two coordinates on the unit hypercube and are constrained to the hyperplane where the sum of the…
This work is concerned with the convex analysis of functions defined on (not necessarily finite-dimensional) Hilbert spaces whose values depend solely on a certain ``spectrum'' of the arguments, a class we term ``spectral functions.'' We…
Spatial statistics is concerned with the analysis of data that have spatial locations associated with them, and those locations are used to model statistical dependence between the data. The spatial data are treated as a single realisation…
Understanding the role that subgradients play in various second-order variational analysis constructions can help us uncover new properties of important classes of functions in variational analysis. Focusing mainly on the behavior of the…
Functional digraphs are unlabelled finite digraphs where each vertex has exactly one out-neighbor. They are isomorphic classes of finite discrete-time dynamical systems. Endowed with the direct sum and product, functional digraphs form a…
One of the main purposes of this article is to give functional equations and differential equations between Bernstein basis functions and generating functions of B-spline curves. Using these equations, very useful formulas containing the…
This paper discusses the dimensions of the spline spaces over T-meshes with lower degree. Two new concepts are proposed: extension of T-meshes and spline spaces with homogeneous boundary conditions. In the dimension analysis, the key…
Consider an $s$-dimensional function being evaluated at $n$ points of a low discrepancy sequence (LDS), where the objective is to approximate the one-dimensional functions that result from integrating out $(s-1)$ variables. Here, the…
In this article, we present a space-frequency theory for spherical harmonics based on the spectral decomposition of a particular space-frequency operator. The presented theory is closely linked to the theory of ultraspherical polynomials on…
We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator $S_K$ on a vector-valued Hardy space $H^{2}(\Omega,K)$ is generated by a quasi-inner function, we also provide relationships of…
Sampling theory in spaces other than the space of band-limited functions has recently received considerable attention. This is in part because the band-limitedness assumption is not very realistic in many applications. In addition,…