Full Müntz theorem in \(L_ p[0,1]\)
type: Item
instance of: scholarly article
title: Full Müntz theorem in \(L_ p[0,1]\)
zbMATH Open document ID: 0852.41004
author: Vladimir A. Operstein
published in: Journal of Approximation Theory
publication date: 1996-06-09T00:00:00Z
review text: The author proves the following theorem, conjectured by P. Borwein and T. Erdélyi: Let \(1< p< \infty\) and \(\{\lambda_i \}^\infty_0\) be a sequence of distinct real numbers greater than \(-1/p\). Then the linear span of the functions \(\{x^{\lambda_i} \}_0^\infty\) is dense in \(L_p [0, 1]\) if and only if \[ \sum^\infty_{i=0} {{\lambda_i+ 1/p} \over {(\lambda_i+ 1/p)^2+ 1}}= \infty. \]
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A30
zbMATH DE Number: 885481
zbMATH Keywords: Müntz theorem
zbMATH Keywords: Lebesgue spaces
reviewed by: David W. Boyd
MaRDI profile type: Publication
full work available at URL: jath.1996.0039
OpenAlex ID: W2025608000
DOI: 10.1006/JATH.1996.0039
Recommended article: The ``full Müntz theorem'' in \(L_p[0,1]\) for \(0<p<\infty\).
Recommended article: The Full Müntz Theorem in C [0, 1] and L 1 [0, 1]
Recommended article: Müntz-Jackson theorems in \(L_ p (0,1), 1 \leq{} p < 2\)
Recommended article: Q4531680
Recommended article: Q4400655
Recommended article: The ``Full Müntz theorem'' revisited
Recommended article: Müntz spaces and Remez inequalities
Recommended article: The Bishop-Phelps-Bollobás theorem for \(\mathcal L(L_1 (\mu), L_\infty [0,1])\)
Recommended article: Paley–Wiener theorem for functions inLp(ℝn)
Recommended article: A uniform boundedness theorem for \(L^\infty(\mu,E)\)
description: scientific article; zbMATH DE number 885481