Related papers: Best approximation in the mean by analytic and har…

We show that Hermite's approximations to values of the exponential function at given algebraic numbers are nearly optimal when considered from an adelic perspective. We achieve this by taking into account the ratio of these values whenever…

We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.

The suitable basis functions for approximating periodic function are periodic, trigonometric functions. When the function is not periodic, a viable alternative is to consider polynomials as basis functions. In this paper we will point out…

In this paper, we present an overview of the recent developments of functional quantization of stochastic processes, with an emphasis on the quadratic case. Functional quantization is a way to approximate a process, viewed as a…

We study integration and $L^2$-approximation of functions of infinitely many variables in the following setting: The underlying function space is the countably infinite tensor product of univariate Hermite spaces and the probability measure…

Given a list of N numbers, the maximum can be computed in N iterations. During these N iterations, the maximum gets updated on average as many times as the Nth harmonic number. We first use this fact to approximate the Nth harmonic number…

We begin by shortly recalling a generalized mean value inequality for subharmonic functions, and two applications of it: first a weighted boundary behavior result (with some new references and remarks), and then a borderline case result to…

Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…

In computational practice, most attention is paid to rational approximations of functions and approximations by the sum of exponents. We consider a wide enough class of nonlinear approximations characterized by a set of two required…

Upper semicontinuous (usc) functions arise in the analysis of maximization problems, distributionally robust optimization, and function identification, which includes many problems of nonparametric statistics. We establish that every usc…

Left and right-continuous functions play an important role in Real analysis, especially in Measure Theory and Integration on the real line and in Stochastic processes indexed by a continuous real time. Semi-continuous functions are also of…

We determine the Lagrange function in Taylor polynomial approximation by solving an appropriate initial-value problem. Hence, we determine the remainder term which we then approximate by means of a natural cubic spline. This results in a…

In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root square mean, etc. Considering the difference of these means, we can establish. some inequalities among them. Interestingly, the difference of…

We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments. This problem has important applications in several areas of numerical…

We study the question of the existence of a dual extremal function for a bounded matrix function on the unit circle in connection with the problem of approximation by analytic matrix functions. We characterize the class of matrix functions,…

We give several characterizations of holomorphic mean Besov-Lipschitz space on the unit ball in $\cn $ and appropriate Besov-Lipschitz space and prove the equivalences between them. Equivalent norms on the mean Besov-Lipschitz space involve…

This paper concerns the universal approximation property with neural networks in variable Lebesgue spaces. We show that, whenever the exponent function of the space is bounded, every function can be approximated with shallow neural networks…

Advancements in modern science have led to an increased prevalence of functional data, which are usually viewed as elements of the space of square-integrable functions $L^2$. Core methods in functional data analysis, such as functional…

While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well developed. Despite increasing demands from applications this…

Over the last decade, approximating functions in infinite dimensions from samples has gained increasing attention in computational science and engineering, especially in computational uncertainty quantification. This is primarily due to the…