Spectral theory for a differential operator: Characteristic determinant and Green's function
type: Item
instance of: scholarly article
title: Spectral theory for a differential operator: Characteristic determinant and Green's function
zbMATH Open document ID: 0707.34014
DOI: 10.1016/0022-247X(89)90186-8
author: John Locker
author: Patrick M. Lang
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: A representation of the Green's function of a two-point differential operator is given in terms of an entire function of \(\lambda\) admitting a power series expansion about any point of \({\mathbb{C}}\) and of the characteristic determinant. This representation is used to calculate the coefficients of the Laurent series of P(\(\lambda\)) about each point in the spectrum of L and to relate the algebraic multiplicity of an eigenvalue \(\lambda_ 0\) to the ascent of the operator \(\lambda_ 0I- L\).
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34L05
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 4161125
zbMATH Keywords: Green's function
zbMATH Keywords: two-point differential operator
zbMATH Keywords: Laurent series
zbMATH Keywords: algebraic multiplicity of an eigenvalue
reviewed by: Gabriella Caristi
MaRDI profile type: Publication
cites work: Q5535091
cites work: On the Nature of the Spectrum of Singular Second Order Linear Differential Equations
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cites work: Spectral representation of the resolvent of a discrete operator
cites work: Spectral theory of two-point differential operators determined by \(-D^ 2\). I: Spectral properties
cites work: Q3769477
cites work: Q5829957
cites work: Q5526189
cites work: Q3966611
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description: scientific article; zbMATH DE number 4161125