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.
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Kurasov, P. Triplet extensions I: Semibounded operators in the scale of Hilbert spaces. J Anal Math 107, 251–286 (2009). https://doi.org/10.1007/s11854-009-0011-6
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DOI: https://doi.org/10.1007/s11854-009-0011-6