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arXiv · 1212.6798

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

Konstantin Pankrashkin
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Abstract

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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BibTeXRIS

Konstantin Pankrashkin. 2013-01-08. An example of unitary equivalence between self-adjoint extensions and their parameters. https://doi.org/10.1016/j.jfa.2013.07.025

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