A necessary condition for the convergence of simple partial fractions in \( L_p(\mathbb R)\)
type: Item
instance of: scholarly article
title: A necessary condition for the convergence of simple partial fractions in \( L_p(\mathbb R)\)
zbMATH Open document ID: 1293.30075
DOI: 10.1134/S0001434612070164
author: Yanyan Li
published in: Mathematical Notes
publication date: 2013-02-22T00:00:00Z
review text: Let \(p>1\) and let \((z_k)\) be a sequence of complex numbers having non-vanishing imaginary part. In the main theorem, the author shows that the condition \[ \sum_{k=1}^\infty \frac{k^{p-1}}{|z_k^*|^{p-1}} < \infty, \] where \((z_k^*)\) is the sequence obtained from \((z_k)\) by arranging \(|z_k|\) in increasing order, is necessary for the convergence of the series \(\sum_{k=1}^\infty 1/(t-z_k)\) of simple partial fractions in \(L_p(\mathbb{R})\).
Mathematics Subject Classification ID: 30E10
Mathematics Subject Classification ID: 41A20
zbMATH DE Number: 6138371
zbMATH Keywords: simple partial fractions
zbMATH Keywords: approximation
zbMATH Keywords: Hilbert transform
reviewed by: Jürgen Müller
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6138371