Related papers: Approximable WAP- and LUC-interpolation sets
We introduce Lipschitz continuous and $C^{1,1}$ geometric approximation and interpolation methods for sampled bounded uniformly continuous functions over compact sets and over complements of bounded open sets in $\mathbb{R}^n$ by using…
The aim of this paper is to extend the approximate quasi-interpolation on a uniform grid by dilated shifts of a smooth and rapidly decaying function on a uniform grid to scattered data quasi-interpolation. It is shown that high order…
We study universal approximation of continuous functionals on compact subsets of products of Hilbert spaces. We prove that any such functional can be uniformly approximated by models that first take finitely many continuous linear…
Unitary best approximation to the exponential function on an interval on the imaginary axis has been introduced recently. In the present work two algorithms are considered to compute this best approximant: an algorithm based on rational…
In this note, we will present global equisingular approximations of quasi-plurisubharmonic functions with stable analytic pluripolar sets on compact complex manifolds.
Interpolation and approximation of functionals with conditionally positive definite kernels is considered on sets of centers that are not determining for polynomials. It is shown that polynomial consistency is sufficient in order to define…
In this paper, we propose an interpolation formula for periodic functions. This formula can be regarded as an analog of the Sinc approximation, which is an interpolation formula for functions defined on the entire infinite interval.…
In Mergelyan type approximation we uniformly approximate functions on compact sets K by polynomials or rational functions or holomorphic functions on varying open sets containing K. In the present paper we consider analogous approximation,…
We obtain a result concerning the stability under the interpolation with functional parameter method for the approximation spaces of Lorentz-Marcinkiewicz type and also for the approximation spaces generated by symmetric norming functions…
We study the uniqueness sets, the weak interpolation sets, and convergence of the Lagrange interpolation series in radial weighted Fock spaces
In the present paper, we examine in detail the method of "graph compactifications" of topological groups. The graph and Ellis methods of constructing proper compactifications of topological groups are applied for the investigation of…
For a topological group G we introduce the algebra SUC(G) of strongly uniformly continuous functions. It contains the algebra WAP(G) of weakly almost periodic functions as well as the algebras LE(G) and Asp(G) of locally equicontinuous and…
We prove a.s. (almost sure) unisolvency of interpolation by continuous random sampling with respect to any given density, in spaces of multivariate a.e. (almost everywhere) analytic functions. Examples are given concerning polynomial and…
We apply the topology of convergence on compact sets to define unpredictable functions [5, 6]. The topology is metrizable and easy for applications with integral operators. To demonstrate the effectiveness of the approach, the existence and…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
Uniform interpolation properties are defined for equational consequence in a variety of algebras and related to properties of compact congruences on first the free and then the finitely presented algebras of the variety. It is also shown,…
We characterize sampling and interpolating sets with derivatives in weighted Fock spaces on the complex plane in terms of their weighted Beurling densities.
In this article we introduce and study uniform and non-uniform approximate lattices in locally compact second countable (lcsc) groups. These are approximate subgroups (in the sense of Tao) which simultaneously generalize lattices in lcsc…
We discuss a selection of recent developments in arithmetic combinatorics having to do with ``approximate algebraic structure'' together with some of their applications.
We study the interpolation group whose elements are suitable pairs of formal power series. This group has a faithful representation into infinite lower triangular matrices and carries thus a natural structure as a Lie group. The matrix…