Almost orthogonality of Birkhoff's solutions
type: Item
instance of: scholarly article
title: Almost orthogonality of Birkhoff's solutions
zbMATH Open document ID: 0789.34070
DOI: 10.1007/BF03322336
author: Arcady Minkin
published in: Results in Mathematics
publication date: 1994-01-13T00:00:00Z
review text: The paper concerns estimates for eigenfunctions for a quasi-differential expression \(I(y) \equiv D_ ny\) where \(D_ n\) is a superposition of first order linear differential expressions with coefficients from \(L(0,1)\). It is proved that a fundamental system of Birkhoff's solutions of an equation \(I(y)=\lambda y\) is almost orthogonal in \(L^ 2(0,1)\). Moreover, for an arbitrary solution \(y\) of the equation \(I(y)= \lambda y\) estimations of the \(L_ p\)-norm of \(D_ ky\) by the \(L_ 2\)-norm of \(D_ jy\) and suitable powers of \(| \rho |\) and \(| im \rho |\) where \(\rho=\lambda^{1 \over n}\) are obtained.
Mathematics Subject Classification ID: 34L10
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 484142
zbMATH Keywords: eigenvalue estimates
zbMATH Keywords: estimates for eigenfunctions
zbMATH Keywords: quasi-differential expression
zbMATH Keywords: superposition of first order linear differential expressions
zbMATH Keywords: fundamental system of Birkhoff's solutions
zbMATH Keywords: almost orthogonal
reviewed by: Teresa Regińska
MaRDI profile type: Publication
cites work: Q3925197
cites work: Q3764481
cites work: Q3717428
cites work: Q5624013
description: scientific article; zbMATH DE number 484142