1212.6798 (Konstantin Pankrashkin)

An example of unitary equivalence between self-adjoint extensions and
their parameters    [PDF]

Konstantin Pankrashkin

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.

View original: http://arxiv.org/abs/1212.6798