Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The big q-Jacobi function transform   We give a detailed description of the resolution of the identity of a second
order $q$-difference operator considered as an unbounded self-adjoint operator
on two different Hilbert spaces. The $q$-difference operator and the two
choices of Hilbert spaces naturally arise from harmonic analysis on the quantum
group $SU_q(1,1)$ and $SU_q(2)$. The spectral analysis associated to
$SU_q(1,1)$ leads to the big $q$-Jacobi function transform together with its
Plancherel measure and inversion formula. The dual orthogonality relations give
a one-parameter family of non-extremal orthogonality measures for the
continuous dual $q^{-1}$-Hahn polynomials with $q^{-1}>1$, and explicit sets of
functions which complement these polynomials to orthogonal bases of the
associated Hilbert spaces. The spectral analysis associated to $SU_q(2)$ leads
to a functional analytic proof of the orthogonality relations and quadratic
norm evaluations for the big $q$-Jacobi polynomials.

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The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph