Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The representer theorem for Hilbert spaces: a necessary and sufficient
  condition   A family of regularization functionals is said to admit a linear representer
theorem if every member of the family admits minimizers that lie in a fixed
finite dimensional subspace. A recent characterization states that a general
class of regularization functionals with differentiable regularizer admits a
linear representer theorem if and only if the regularization term is a
non-decreasing function of the norm. In this report, we improve over such
result by replacing the differentiability assumption with lower semi-continuity
and deriving a proof that is independent of the dimensionality of the space.

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The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
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The categories of this paper are: eess
13
The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th