Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Self-adjoint difference operators and symmetric Al-Salam--Chihara
  polynomials   The symmetric Al-Salam--Chihara polynomials for $q>1$ are associated with an
indeterminate moment problem. There is a self-adjoint second order difference
operator on $\ell^2(\Z)$ to which these polynomials are eigenfunctions. We
determine the spectral decomposition of this self-adjoint operator. This leads
to a class of discrete orthogonality measures, which have been obtained
previously by Christiansen and Ismail using a different method, and we give an
explicit orthogonal basis for the corresponding weighted $\ell^2$-space. In
particular, the orthocomplement of the polynomials is described explicitly.
Taking a limit we obtain all the $N$-extremal solutions to the $q^{-1}$-Hermite
moment problem, a result originally obtained by Ismail and Masson in a
different way. Some applications of the results are discussed.

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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex