Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dixmier Trace Formulas and Negative Eigenvalues of Schroedinger
  Operators on Curved Noncommutative Tori   In a previous paper we established Cwikel-type estimates and the CLR
inequality for noncommutative tori. In this follow-up paper we extend these
results to pseudodifferential operators and to curved noncommutative tori,
where the role of the usual Laplacian is played by Laplace-Beltrami operators
associated with arbitrary densities and Riemannian metrics. The Cwikel
estimates are used to get several $L_2$ and $L_{1^+}$ Dixmier trace formulas.
Here $L_{1^+}$ is meant as the intersection of all $L_p$-spaces with $p>1$.
This extends previous Dixmier trace formulas to the $L_2$ and $L_{1^+}$
settings. Combining the Cwikel estimates with a borderline version of the
Birman-Schwinger principle leads to a CLR-type inequality for the number of
negative eigenvalues of (fractional) Schr\"odinger operators that are built out
of fractional Laplace-Beltrami operators and $L_p$-potentials. We also
conjecture a semi-classical Weyl's law for such operators.

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The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: q-alg