Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unitary equivalence of lowest dimensional reproducing formulae of type
  $\mathcal{E}_2 \subset Sp(2,{\mathbb R})$   All two-dimensional reproducing formulae, i.e. of $L^2({\mathbb R}^2)$,
resulting out of restrictions of the projective metaplectic representation to
connected Lie subgroups of $Sp(2,{\mathbb R})$ and of type $\mathcal{E}_2$,
were listed and classified up to conjugation within $Sp(2,{\mathbb R})$ in [2],
[3]. A full classification, up to conjugation within ${\mathbb R}^2 \rtimes
Sp(1,{\mathbb R})$, of one-dimensional reproducing formulae, i.e. of
$L^2({\mathbb R})$, resulting out of restrictions of the extended projective
metaplectic representation to connected Lie subgroups of ${\mathbb R}^2 \rtimes
Sp(1,{\mathbb R})$ was obtained in [13], [14]. In dimension one, there are no
reproducing formulae with one-dimensional parametrizations, yet in dimension
two, there are reproducing formulae with two-dimensional parametrizations.
Two-dimensional reproducing subgroups of $Sp(2,{\mathbb R})$ of type
$\mathcal{E}_2$ are a novelty. They exhibit completely new phase space
phenomena. We show, that they are all unitarily equivalent via natural choices
of coordinate systems, and we derive the consequences of this equivalence.

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The categories of this paper are: eess
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
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The categories of this paper are: econ
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex