Eigenfunction expansions associated with an operator differential equation nonlinearly depending on a spectral parameter
type: Item
instance of: scholarly article
zbMATH Open document ID: 1313.34276
author: Volodymyr Khrabustovskyi
publication date: 2014-08-21T00:00:00Z
full work available at URL: https://arxiv.org/abs/1307.5460
Mathematics Subject Classification ID: 34L10
Mathematics Subject Classification ID: 34B07
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 6333573
zbMATH Keywords: operator-differential equation
zbMATH Keywords: Nevanlinna function
zbMATH Keywords: eigenfunction expansions
MaRDI profile type: Publication
arXiv ID: 1307.5460
arXiv classification: math.SP
arXiv classification: math.CA
arXiv classification: math.FA
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title: Eigenfunction expansions associated with an operator differential equation nonlinearly depending on a spectral parameter
published in: Methods of Functional Analysis and Topology
review text: The author obtains eigenfunction expansions for operator-differential equations of the form NEWLINE\[NEWLINEl[y]-\lambda m[y]-n_\lambda [y]=m[f],NEWLINE\]NEWLINE where \(l,m,n_\lambda\) are symmetric differential expressions with bounded operator coefficients on a Hilbert space, \(n_\lambda\) is a Nevanlinna function of the spectral parameter \(\lambda\). The case \(n_\lambda =0\) was considered in the same generality in the author's earlier paper [Methods Funct. Anal. Topol. 15, No. 2, 137--151 (2009; Zbl 1199.34450)].
reviewed by: Anatoly N. Kochubei
description: scientific article; zbMATH DE number 6333573