Indefinite boundary eigenvalue problems in a Pontrjagin space setting
type: Item
instance of: scholarly article
title: Indefinite boundary eigenvalue problems in a Pontrjagin space setting
zbMATH Open document ID: 0982.47029
DOI: 10.1007/BF03322823
author: Albert Schneider
author: Rolf Vonhoff
published in: Results in Mathematics
publication date: 2002-07-02T00:00:00Z
review text: We study eigenvalue problems \(Fy=\lambda Gy\) consisting of Hamiltonian systems of ordinary differential equations on a compact interval with symmetric \(\lambda\)-linear boundary conditions. The problems we are interested in are non-definite: neither left- nor right-definite. Instead of this, we give some weak condition on one coefficient of the Hamiltonian system which ensures that a Hermitian form associated with the operator \(F\) has at most finitely many negative squares. This enables us to study the problem by the help of a compact self-adjoint operator in a Pontryagin space and we obtain as a main result uniformly convergent eigenfunction expansions. In the final section, applications to formally self-adjoint differential equations of higher-order are given.
reviewed by: Trandafir Balan
Mathematics Subject Classification ID: 47B50
Mathematics Subject Classification ID: 46C20
Mathematics Subject Classification ID: 47B07
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 34L10
Mathematics Subject Classification ID: 47A75
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 1320609
zbMATH Keywords: eigenvalue problems
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: ordinary differential equations
zbMATH Keywords: compact self-adjoint operator
zbMATH Keywords: Pontryagin space
zbMATH Keywords: uniformly convergent eigenfunction expansions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1320609