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

作者：Pankrashkin Konstantin^*

来源：Journal of Functional Analysis, 2013, 265(11): 2910-2936.

DOI：10.1016/j.jfa.2013.07.025

• Self-adjoint extension
• Unitary equivalence
• Metric graph
• Laplacian
• Boundary conditions
• Boundary triplet
• Weyl function

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 the parameterizing boundary operator acting in a smaller space, and one is able to provide an explicit form for the associated unitary transform. Applications to differential operators on metric graphs and to direct sums are discussed.

• 出版日期2013-12-1