Riesz type kernels over the ring of integers of a local field
type: Item
instance of: scholarly article
title: Riesz type kernels over the ring of integers of a local field
zbMATH Open document ID: 0883.43011
author: Shijun Zheng
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-03-16T00:00:00Z
review text: The Riesz kernels of order \((\mu, \lambda)\) over the ring of integers of a local field \(O\) are studied in this paper: \[ \gamma_{\mu, \lambda,n} (x)= \sum^{n-1}_{k=0} \left(1- {k \choose n}^\mu \right)^\lambda \chi_k(x), \] for \(\mu>0\), \(\lambda>0\), and \[ \widetilde \gamma_{\mu,n} (x)= \sum^{n-1}_{k=0} \biggl(1- \bigl|u(k)u(n)^{-1}\bigr |^\mu \biggr) \chi_k(x), \] for \(\mu>0\). Also, the convolution Riesz means operators and the Riesz means of type I \[ \begin{gathered} R_{\mu, \lambda,n} f(x)= \gamma_{\mu, \lambda, n}*f(x), \\ \widetilde R_{\mu,n} (x)f(x)= \widetilde\gamma_{\mu,n}*f(x)\end{gathered} \] are considered. The main results in this note are approximation theorems for these two kinds of convolution Riesz means and the approximation orders for the Lip-functions are given.
Mathematics Subject Classification ID: 43A70
zbMATH DE Number: 1031588
zbMATH Keywords: Riesz kernels
zbMATH Keywords: convolution Riesz means operators
zbMATH Keywords: Riesz means
reviewed by: Su Weiyi
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5352
OpenAlex ID: W1990097223
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DOI: 10.1006/JMAA.1997.5352
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description: scientific article; zbMATH DE number 1031588