Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the density of polyharmonic splines   This article treats the question of fundamentality of the translates of a
polyharmonic spline kernel (also known as a surface spline) in the space of
continuous functions on a compact set $\Omega\subset \RR^d$ when the translates
are restricted to $\Omega$. Fundamentality is not hard to demonstrate when a
low degree polynomial may be added or when translates are permitted to lie
outside of $\Omega$; the challenge of this problem stems from the presence of
the boundary, for which all successful approximation schemes require an added
polynomial.
  When $\Omega$ is the unit ball, we demonstrate that translates of
polyharmonic splines are fundamental by considering two related problems: the
fundamentality in the space of functions vanishing at the boundary and
fundamentality of the restricted kernel in the space of continuous function on
the sphere. This gives rise to a new approximation scheme composed of two
parts: one which approximates purely on $\partial \Omega$, and a second part
involving a shift invariant approximant of a function vanishing outside of a
neighborhood $\Omega$.

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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
0
The categories of this paper are: hep-ph