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

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.

25 pages. Misprints corrected, references added

References in corpus (4)

• Spectra of self-adjoint extensions and applications to solvable Schroedinger operators
• Unitary dimension reduction for a class of self-adjoint extensions with applications to graph-like structures
• The spectrum of the Hilbert space valued second derivative with general self-adjoint boundary conditions
• Equilateral quantum graphs and boundary triples

Cited by in corpus (9)

• Spectral Theory of Infinite Quantum Graphs
• Scattering on periodic metric graphs
• Cantor spectrum of graphene in magnetic fields
• Spectral Estimates for Infinite Quantum Graphs
• New relations between discrete and continuous transition operators on (metric) graphs
• Spectra of magnetic chain graphs: coupling constant perturbations
• Spectral properties of magnetic chain graphs
• Embedded trace operator for infinite metric trees
• The Jacobi operator and its Donoghue $m$-functions