Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Systems of reproducing kernels and their biorthogonal: completeness or
  incompleteness?   Let $\{v_n\}$ be a complete minimal system in a Hilbert space $\mathcal{H}$
and let $\{w_m\}$ be its biorthogonal system. It is well known that $\{w_m\}$
is not necessarily complete. However the situation may change if we consider
systems of reproducing kernels in a reproducing kernel Hilbert space
$\mathcal{H}$ of analytic functions. We study the completeness problem for a
class of spaces with a Riesz basis of reproducing kernels and for model
subspaces $K_\Theta$ of the Hardy space. We find a class of spaces where
systems biorthogonal to complete systems of reproducing kernels are always
complete, and show that in general this is not true. In particular we answer
the question posed by N.K. Nikolski and construct a model subspace with a
non-complete biorthogonal system.

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The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat