Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractional Laplacian with Hardy potential   We give sharp two-sided estimates of the semigroup generated by the
fractional Laplacian plus the Hardy potential on $\mathbb{R}^d$, including the
case of the critical constant. We use Davies' method back-to-back with a new
method of integral analysis of Duhamel's formula.

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The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: cond-mat