Limit properties of eigenvalues in spectral gaps

Seppo Hassi*, Henk de Snoo, Henrik Winkler

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review


Let S be a closed symmetric operator or relation with defect numbers (1, 1). The selfadjoint extensions A(τ) of S are parametrized over τ ∈ ℝ∪{∞}. When the selfadjoint extension A(0) has a spectral gap (α, β), then the same is true for all the other selfadjoint extensions A(τ) of S with the possible exception of an isolated eigenvalue λ(τ) of A(τ). The limiting properties of this isolated eigenvalue are studied in terms of τ.

Original languageEnglish
Title of host publicationIndefinite Inner ProductSpaces, Schur Analysis,and Differential Equations
Subtitle of host publicationA Volume Dedicated to Heinz Langer
EditorsDaniel Alpay, Bernd Kirstein
Place of PublicationBirkhäuser, Cham
PublisherSpringer International Publishing
Number of pages21
ISBN (Electronic)978-3-319-68849-7
ISBN (Print)978-3-319-68848-0
Publication statusPublished - 1-Jan-2018

Publication series

NameOperator Theory: Advances and Applications
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878


  • Asymptotic expansion
  • Moment
  • Nevanlinna function
  • Selfadjoint extension
  • Spectral gap
  • Spectral measure
  • Symmetric operator


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