On approximation of entire functions by exponential polynomials
type: Item
instance of: scholarly article
title: On approximation of entire functions by exponential polynomials
zbMATH Open document ID: 0833.32001
DOI: 10.1007/BF02336888
published in: Lithuanian Mathematical Journal
publication date: 1995-11-07T00:00:00Z
review text: Let \(K\) be a compact set in \(\mathbb{R}^n\) and \(B_K\) be a set of all continuous bounded functions on \(\mathbb{R}^n\), whose spectrum belongs to \(K\). The author investigates the question of approximation of the function \(f \in B_{K}\) on arbitrary compact sets \(S \subset \mathbb{R}^n\) by finite exponential sums \[ P_m(x) = \sum_\nu C^{(m)}_\nu e^{i\langle \alpha^{(m)} \nu, x\rangle},\;\nu \in \mathbb{Z},\;\alpha^{(m)} \in (0,\varepsilon), \] which additionally satisfy the condition \(\sup \{|P_m(x) |: x \in \mathbb{R}^n\} \leq \sup \{|f(x)|: x\in \mathbb{R}^n\}\). Some estimates of the rate of the approximation are given. The case of convex compact \(K\) is considered separately.
Mathematics Subject Classification ID: 32A15
Mathematics Subject Classification ID: 32E30
Mathematics Subject Classification ID: 41A10
zbMATH DE Number: 813158
zbMATH Keywords: Levitan's polynomial
zbMATH Keywords: exponential sums
zbMATH Keywords: approximation of entire functions
author: Saulius Norvidas
MaRDI profile type: Publication
cites work: Differential inequalities in Banach spaces of entire functions. I
cites work: Q5823611
cites work: Finite Type Functions as Limits of Exponential Sums
cites work: Distributions semi-régulières et changements de coordonnees
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description: scientific article; zbMATH DE number 813158