Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonnegative $C^2(\mathbb{R}^2)$ interpolation   In this paper, we prove two improved versions of the Finiteness Principle for
nonnegative $ C^2(\mathbb{R}^2) $ interpolation, previously proven by
Fefferman, Israel, and Luli. The first version sharpens the finiteness constant
to $ 64 $, and the second version carries better computational practicality.
Along the way, we also provide detailed construction of nonnegative $ C^2 $
interpolants in one-dimension, and prove the nonexistence of a bounded linear $
C^2 $-extension operator that preserves nonnegativity.

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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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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: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con