On the Muckenhoupt condition
type: Item
instance of: scholarly article
title: On the Muckenhoupt condition
zbMATH Open document ID: 0644.46014
DOI: 10.1007/BF01849033
published in: Periodica Mathematica Hungarica
publication date: 1987-01-01T00:00:00Z
review text: A system \((\phi_ n)_{n\in {\mathbb{Z}}}\) is called a Riesz basis of a Hilbert space H if it is complete and for finite sequences \((c_ n)\) of complex numbers \(\| \sum c_ n\phi_ n\|^ 2\) is of the same order as \(\sum | c_ n|^ 2\). Systems of the form \((E^{i\lambda_ nx},xe^{i\lambda_ nx},...,x^{m_ n- 1}e^{i\lambda_ nx})_{n\in {\mathbb{Z}}}\), where \(\lambda_ n\) is complex, \(m_ n\) is a positive integer (which arise when solving systems of linear differential equations) are of interest for \(H=L^ 2(0,a)\). Several results are quoted which ensure such a system is a Riesz basis. The aim of the paper is to prove a converse of one of these results.
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 30B50
Mathematics Subject Classification ID: 46B15
Mathematics Subject Classification ID: 30D15
zbMATH DE Number: 4050272
zbMATH Keywords: Muckenhoupt condition
zbMATH Keywords: entire functions of exponential type
zbMATH Keywords: indicator diagram
zbMATH Keywords: Riesz basis of a Hilbert space
author: Barnabás Apagyi
MaRDI profile type: Publication
cites work: Q5833361
full work available at URL: https://doi.org/10.1007/bf01849033
OpenAlex ID: W2024786258
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description: scientific article; zbMATH DE number 4050272