A generalization of Krein`s extension formalism for symmetric relations with deficiency index (1,1)

2024/07/10 by Emmel, Christian
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2407.07491

Abstract

Let S be a symmetric relation with deficiency index (1,1). In this article, we extend Krein`s resolvent formalism in order to describe all, not necessarily self-adjoint, extensions S ⊂ A with \varrho(A)≠ ∅. The corresponding Q-functions turn out to be quasi-Herglotz functions. We will use their structure to characterize the spectrum of such extensions. Finally, we also provide a model for such an extension on a reproducing kernel Hilbert space when S is simple.

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