Triplet extensions I: Semibounded operators in the scale of Hilbert spaces

Research output: Contribution to journalArticle

Abstract

The extension theory for semibounded symmetric operators is generalized by including operators acting in a triplet of Hilbert spaces. We concentrate our attention on the case where the minimal operator is essentially self-adjoint in the basic Hilbert space and construct a family of its self-adjoint extensions inside the triplet. All such extensions can be described by certain boundary conditions, and a natural counterpart of Krein's resolvent formula is obtained.

Details

Authors
  • Pavel Kurasov
Organisations
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Mathematics
Original languageEnglish
Pages (from-to)251-286
JournalJournal d'Analyse Mathematique
Volume107
Issue number1
Publication statusPublished - 2009
Publication categoryResearch
Peer-reviewedYes