Spectral theory of two-point differential operators determined by \(-D^ 2\). I: Spectral properties
type: Item
instance of: scholarly article
title: Spectral theory of two-point differential operators determined by \(-D^ 2\). I: Spectral properties
zbMATH Open document ID: 0707.34015
DOI: 10.1016/0022-247X(89)90196-0
author: John Locker
author: Patrick M. Lang
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: The authors develop the tools for the complete resolution of the spectral theory for differential operators L in \(L^ 2(0,1)\) of the form: \({\mathcal D}(L)=\{u\in H^ 2(0,1):\) \(B_ iu=0\), \(i=1,2\}\), \(LU=-u''\), where \(H^ 2(0,1)\) denotes the usual Sobolev space and \(B_ 1\) and \(B_ 2\) are linearly independent boundary operators of the form \[ B_ 1(u)=a_ 1u'(0)+b_ 1u'(1)+a_ 0u(0)+b_ 0u(1) \] \[ B_ 2(u)=c_ 1u'(0)+d_ 1u'(1)+c_ 0u(0)+d_ 0u(1). \] The work is based on six numerical parameters, defined in terms of the coefficients of \(B_ 1\) and \(B_ 2\), which intervene in the development of the characteristic determinant of L, in the Green's function and in other spectral quantities. At the end of the paper, a complete classification scheme of spectral properties of L is given. Proofs will appear in the second part.
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34L05
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 4161126
zbMATH Keywords: spectral theory
zbMATH Keywords: Sobolev space
zbMATH Keywords: Green's function
reviewed by: Gabriella Caristi
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4161126