Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An example of unitary equivalence between self-adjoint extensions and
  their parameters   The spectral problem for self-adjoint extensions is studied using the
machinery of boundary triplets. For a class of symmetric operators having Weyl
functions of a special type we calculate explicitly the spectral projections in
the form of operator-valued integrals. This allows one to give a constructive
proof of the fact that, in certain intervals, the resulting self-adjoint
extensions are unitarily equivalent to a certain parameterizing operator acting
in a smaller space, and one is able to provide an explicit form the associated
unitary transform. Applications to differential operators on metric graphs and
to direct sums are discussed.

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The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph