Semiclassical approximation for a nonself-adjoint Sturm-Liouville problem with a parabolic potential
type: Item
instance of: scholarly article
title: Semiclassical approximation for a nonself-adjoint Sturm-Liouville problem with a parabolic potential
zbMATH Open document ID: 1192.34032
DOI: 10.1134/S0001434609090181
author: V. I. Pokotilo
author: A. A. Shkalikov
published in: Mathematical Notes
publication date: 2010-01-12T00:00:00Z
review text: The authors analyze the spectral behavior of the corresponding family of differential operators \(L(\varepsilon )y=i\varepsilon y^{\prime \prime }+q(x)y,\) \(\varepsilon >0\), on the interval \([a,b]\) with the boundary conditions \(y(a)=y(b)\) as \(\varepsilon \rightarrow 0\) for the case in which \(q(x)\) is an analytic function with one extremum on \([a,b]\). For this model problem the authors find the limit spectral graph (the limit curves along which the spectrum is concentrated).
reviewed by: Bilender P. Allahverdiev
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34L15
Mathematics Subject Classification ID: 34L20
Mathematics Subject Classification ID: 34L40
zbMATH DE Number: 5656346
zbMATH Keywords: Sturm-Liouville problem
zbMATH Keywords: Orr-Sommerfeld operator
zbMATH Keywords: spectral graph
zbMATH Keywords: velocity profile
zbMATH Keywords: small parameter
zbMATH Keywords: analytic function
zbMATH Keywords: Stokes lines
zbMATH Keywords: entire function
MaRDI profile type: Publication
cites work: Q3324254
description: scientific article; zbMATH DE number 5656346