Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590647 | Journal of Functional Analysis | 2013 | 27 Pages |
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 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Konstantin Pankrashkin,