Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kernel Approximation on Manifolds I: Bounding the Lebesgue Constant   The purpose of this paper is to establish that for any compact, connected
C^{\infty} Riemannian manifold there exists a robust family of kernels of
increasing smoothness that are well suited for interpolation. They generate
Lagrange functions that are uniformly bounded and decay away from their center
at an exponential rate. An immediate corollary is that the corresponding
Lebesgue constant will be uniformly bounded with a constant whose only
dependence on the set of data sites is reflected in the mesh ratio, which
measures the uniformity of the data.
  The analysis needed for these results was inspired by some fundamental work
of Matveev where the Sobolev decay of Lagrange functions associated with
certain kernels on \Omega \subset R^d was obtained. With a bit more work, one
establishes the following: Lebesgue constants associated with surface splines
and Sobolev splines are uniformly bounded on R^d provided the data sites \Xi
are quasi-uniformly distributed. The non-Euclidean case is more involved as the
geometry of the underlying surface comes into play. In addition to establishing
bounded Lebesgue constants in this setting, a "zeros lemma" for compact
Riemannian manifolds is established.

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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: stat