Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Addendum to 'The equivariant spectral function of an invariant elliptic
  operator'   Let $M$ be a compact boundaryless Riemannian manifold, carrying an effective
and isometric action of a torus $T$, and $P_0$ an invariant elliptic classical
pseudodifferential operator on $M$. In this note, we strengthen asymptotics for
the equivariant (or reduced) spectral function of $P_0$ derived previously,
which are already sharp in the eigenvalue aspect, to become almost sharp in the
isotypic aspect. In particular, this leads to hybrid equivariant $L^p$-bounds
for eigenfunctions that are almost sharp in the eigenvalue and isotypic aspect.

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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: econ