Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dispersive estimates for Dirac Operators in dimension three with
  obstructions at threshold energies   We investigate $L^1\to L^\infty$ dispersive estimates for the three
dimensional Dirac equation with a potential. We also classify the structure of
obstructions at the thresholds of the essential spectrum as being composed of a
two dimensional space of resonances and finitely many eigenfunctions. We show
that, as in the case of the Schr\"odinger evolution, the presence of a
threshold obstruction generically leads to a loss of the natural $t^{-\frac32}$
decay rate. In this case we show that the solution operator is composed of a
finite rank operator that decays at the rate $t^{-\frac12}$ plus a term that
decays at the rate $t^{-\frac32}$.

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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
5
The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn