On the convergence of biorthogonal series related to odd-order differential operators with nonsmooth coefficients
type: Item
instance of: scholarly article
title: On the convergence of biorthogonal series related to odd-order differential operators with nonsmooth coefficients
zbMATH Open document ID: 1204.47050
DOI: 10.1134/S1064562410020079
author: S. V. Afonin
author: I. Lomov
published in: Doklady Mathematics
publication date: 2010-11-17T00:00:00Z
review text: Let \({\mathcal L}\) be a differential operator generated by \[ \ell u \equiv u^{(n)}(x) +\sum_{k=0}^{n-1} a_k(x) u^{(k)}(x),\quad x\in G=(0,1), \] which acts on the class \(D_n\) of functions which are absolutely continuous on \([0,1]\) together with their derivatives up to order \(n-1.\) Here, \(a_{n-1}\in L^s(G)\) with \(s\geq1,\) \(a_k(x)\in L(G)\) for \(k=0,1,\dots,n-2\), where \(n=2l+1\) for some non-negative integer \(l.\) The authors estimate the rate of equiconvergence of spectral decompositions in root functions of the operator \({\mathcal L}.\)
reviewed by: Dian K. Palagachev
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 5816897
zbMATH Keywords: biorthogonal series
zbMATH Keywords: differential operator
zbMATH Keywords: nonsmooth coefficients
MaRDI profile type: Publication
cites work: The local convergence of biorthogonal series related to differential operators with nonsmooth coefficients. II
cites work: Convergence of biorthogonal expansions of functions on an interval for higher-order differential operators
cites work: Shift formulas for root functions of odd-order differential operators with nonsmooth coefficients
description: scientific article; zbMATH DE number 5816897