Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extensions of symmetric operators I: The inner characteristic function
  case   Given a symmetric linear transformation on a Hilbert space, a natural problem
to consider is the characterization of its set of symmetric extensions. This
problem is equivalent to the study of the partial isometric extensions of a
fixed partial isometry. We provide a new function theoretic characterization of
the set of all self-adjoint extensions of any symmetric linear transformation
$B$ with equal indices and inner Livsic characteristic function $\Theta _B$ by
constructing a natural bijection between the set of self-adjoint extensions and
the set of all contractive analytic functions $\Phi$ which are greater or equal
to $\Theta _B$. In addition we characterize the set of all symmetric extensions
$B'$ of $B$ which have equal indices in the case where $\Theta _B$ is inner.

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The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int