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On the adjoint of a symmetric operator

Behrndt, Jussi and Langer, Matthias (2010) On the adjoint of a symmetric operator. Journal of the London Mathematical Society, 82 (3). pp. 563-580.

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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.