Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-Adjoint Operators in Extended Hilbert Spaces $H\oplus W$: An
  Application of the General GKN-EM Theorem   We construct self-adjoint operators in the direct sum of a complex Hilbert
space $H$ and a finite dimensional complex inner product space $W$. The
operator theory developed in this paper for the Hilbert space $H\oplus W$ is
originally motivated by some fourth-order differential operators, studied by
Everitt and others, having orthogonal polynomial eigenfunctions. Generated by a
closed symmetric operator $T_{0}$ in $H$ with equal and finite deficiency
indices and its adjoint $T_{1}$, we define \textit{families} of minimal
operators $\{\widehat{T}_{0}\}$ and maximal operators $\{\widehat{T}_{1}\}$ in
the extended space $H\oplus W$ and establish, using a recent theory of complex
symplectic geometry, developed by Everitt and Markus, a characterization of
self-adjoint extensions of $\{\widehat{T}_{0}\}$ when the dimension of the
extension space $W$ is not greater than the deficiency index of $T_{0}$. A
generalization of the classical Glazman-Krein-Naimark (GKN) Theorem - called
the GKN-EM Theorem to acknowledge the work of Everitt and Markus - is key to
finding these self-adjoint extensions in $H\oplus W.$ We consider several
examples to illustrate our results.

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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin