NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2013, 4 (6), P. 747–759
WEYL FUNCTION FOR SUM OF OPERATORS TENSOR PRODUCTS
A. A. Boitsev – Saint Petersburg National Research University of Information Technologies, Mechanics and Optics, 49 Kronverkskiy, Saint Petersburg, 197101, Russia; boitsevanton@gmail.com
H. Neidhardt – Weierstrass Institute for Applied Analysis and Stochastic, Berlin, Germany; hagen.neidhardt@wias-berlin.de
I.Yu. Popov – Saint Petersburg National Research University of Information Technologies, Mechanics and Optics, 49 Kronverkskiy, Saint Petersburg, 197101, Russia; popov1955@gmail.com
The boundary triplets approach is applied to the construction of self-adjoint extensions of the operator having the form S = A ⊗ IT + IA ⊗ T where the operator A is symmetric and the operator T is bounded and self-adjoint. The formula for the γ-field and the Weyl function corresponding the the boundary triplet ΠS is obtained in terms of the γ-field and the Weyl function corresponding to the boundary triplet ΠA.
Keywords: operator extension, Weyl function, boundary triplet.
PACS 03.65 Nk