On the adjoint of a symmetric operator

Jussi Behrndt, Matthias Langer

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

In general it is a non-trivial task to determine the adjoint S* of an unbounded symmetric operator S in a Hilbert or Krein space. We propose a method to specify S* explicitly which makes use of two boundary mappings that satisfy an abstract Green's identity and a surjectivity condition, and give rise to a self-adjoint extension of S. We show for various concrete examples how convenient and easily applicable this technique is.
LanguageEnglish
Pages563-580
Number of pages18
JournalJournal of the London Mathematical Society
Volume82
Issue number3
Early online date15 Sep 2010
DOIs
Publication statusPublished - 2010

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Krein Space
Surjectivity
Self-adjoint Extension
Symmetric Operator
Unbounded Operators
Hilbert space

Keywords

  • symmetric operator
  • adjoint
  • self-adjoint extension
  • boundary mappings
  • Green's identity
  • surjectivity condition

Cite this

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On the adjoint of a symmetric operator. / Behrndt, Jussi; Langer, Matthias.

In: Journal of the London Mathematical Society, Vol. 82, No. 3, 2010, p. 563-580.

Research output: Contribution to journalArticle

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KW - self-adjoint extension

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KW - surjectivity condition

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