Distribution of the spectrum of a quadratic pencil
type: Item
instance of: scholarly article
title: Distribution of the spectrum of a quadratic pencil
zbMATH Open document ID: 0721.34099
author: S. A. El-Sharkavi
published in: Moscow University Mathematics Bulletin
publication date: 1989-01-01T00:00:00Z
review text: The problem \(Ly=-y''+q(x)y+i\lambda \alpha (x)y'+\lambda^ 2y=0\) \(- \infty <x<\infty,\) where \(\lambda\) is a spectral parameter and \(y=y(x)\), \(| \alpha (x)| \leq 2\) and q(x) is a continuous regular function \((0<q(x)\to \infty\) as \(| x| \to \infty)\) is investigated. The method of investigating is analytical and is based on estimate of the kernel of the resolvent of the operator L(\(\lambda\)) and application of Tauberian theorems. As a result of the asymptotic behavior of the function N(\(\lambda\)), the distribution of eigenvalues is received.
Mathematics Subject Classification ID: 34L20
zbMATH DE Number: 4188292
zbMATH Keywords: differential operator
zbMATH Keywords: quadratic pencil
zbMATH Keywords: spectral parameter
zbMATH Keywords: Tauberian theorems
zbMATH Keywords: distribution of eigenvalues
MaRDI profile type: Publication
description: scientific article