相关论文: Best approximation in the mean by analytic and har…

We consider the pointwise approximation of a subharmonic function by the logarithm of the modulus of an entire function up to a bounded quantity. In the case of finite order an estimate from below of the planar Lebesgue measure of an…

Let u be a subharmonic function in D={|z|<1}. There exist an absolute constant C and an analytic function f in D such that \int_D |u(z)-log|f(z)|| dm(z)<C where m denotes the plane Lebesgue measure. We also consider uniform approximation.

We consider approximation or recovery of functions based on a finite number of function evaluations. This is a well-studied problem in optimal recovery, machine learning, and numerical analysis in general, but many fundamental insights were…

We present one of the approaches to find the best approximation of the given function by trigonometric polynomials in $L^1$ metric and applied it to find the optimal constants in the Nikolsky's type inequality, concerning approximation of…

For various Hilbert spaces of analytic functions on the unit disk, we characterize when a function $f$ has optimal polynomial approximants given by truncations of a single power series. We also introduce a generalized notion of optimal…

Our goal is to finally settle the persistent problem in Diophantine Approximation of finding best linear approximates. Classical results from the theory of continued fractions provide the solution for the special homogeneous case in the…

A common problem in applied mathematics is to find a function in a Hilbert space with prescribed best approximations from a finite number of closed vector subspaces. In the present paper we study the question of the existence of solutions…

We consider the problem of approximating a function using Herglotz wave functions, which are a superposition of plane waves. When the discrepancy is measured in a ball, we show that the problem can essentially be solved by considering the…

Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…

We study the best approximation problem: \[ \displaystyle \min_{\alpha\in \mathbb R^m}\max_{1\leq i\leq n}\left|y_i -\sum_{j=1}^m \alpha_j \Gamma_j ({\bf x}_i) \right|. \] Here: $\Gamma:=\left\{\Gamma_1,...,\Gamma_m\right\}$ is a list of…

Approximation in measure is employed to solve an asymptotic Dirichlet problem on arbitrary open sets and to show that many functions, including the Riemann zeta-function, are universal in measure. Connections with the Riemann Hypothesis are…

The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods…

We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…

A new analytical approximation function is proposed to accurately fit the solution of a fractional differential equation of order one-half, whose nonhomogeneous term is defined by a modified Bessel function of the first kind. The exact…

Approximation theory is concerned with the ability to approximate functions by simpler and more easily calculated functions. The first question we ask in approximation theory concerns the {\it possibility of approximation}. Is the given…

We study the question of constructive approximation of the harmonic measure $\omega_x^\Omega$ of a connected bounded domain $\Omega$ with respect to a point $x\in\Omega$. In particular, using a new notion of computable harmonic…

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 work, we propose an extensive numerical study on approximating the absolute value function. The methods presented in this paper compute approximants in the form of rational functions and have been proposed relatively recently, e.g.,…

We study the problem of estimating the average of a Lipschitz continuous function $f$ defined over a metric space, by querying $f$ at only a single point. More specifically, we explore the role of randomness in drawing this sample. Our goal…

Let $L^p(\mathbf{T})$ be the Lesbegue space of complex-valued functions defined in the unit circle $\mathbf{T}=\{z: |z|=1\}\subseteq \mathbb{C}$. In this paper, we address the problem of finding the best constant in the inequality of the…