najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМОnajo-1053Research ArticleMATHEMATICSМАТЕМАТИКАWeyl function for sum of operators tensor productsBoitsevA. A.

49, Kronverkskiy, Saint Petersburg, 197101.

boitsevanton@gmail.comNeidhardtH.

Berlin.

hagen.neidhardt@wias-berlin.dePopovI. Yu.

49, Kronverkskiy, Saint Petersburg, 197101.

popov1955@gmail.comSaint Petersburg National Research University of Information Technologies, Mechanics and OpticsRussian FederationWeierstrass Institute for Applied Analysis and StochasticGermany20131708202546747759Copyright © Boitsev A.A., Neidhardt H., Popov I.Y., 20252025Boitsev A.A., Neidhardt H., Popov I.Y.Boitsev A.A., Neidhardt H., Popov I.Y.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1053

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.

operator extensionWeyl functionboundary tripletSupported by Federal Targeted Program ”Scientific and Educational Human Resources for Innovation-Driven Russia” (contract 16.740.11.0030), grant 11-08-00267 of Russian Foundation for Basic Researches and grants of the President of Russia (state contract 14.124.13.2045-MK and grant MK-1493.2013.1), by Program of Development of Leading Russian Universities. A part of this work was made during visits of IYP and AAB to Berlin. We thank WIAS Berlin for kind hospitality.ReferencesM.S.Birman, M.Z.Solomyak. Spectral Theory of Selfadjoint Operators in Hilbert Space. Kluwer, Dordrecht (1987).M.S.Birman, M.Z.Solomyak. Spectral Theory of Selfadjoint Operators in Hilbert Space. Kluwer, Dordrecht (1987).Konrad Schmu¨dgen. Unbounded self-adjoint operators on Hilbert space, volume 265 of Graduate Texts in Mathematics. Springer, Dordrecht, 2012.Konrad Schmu¨dgen. Unbounded self-adjoint operators on Hilbert space, volume 265 of Graduate Texts in Mathematics. Springer, Dordrecht, 2012.B.S.Pavlov. Operator extensions theory and explicitly solvable models. Uspekhi Mat. Nauk. 42 (6). P. 99-131 (1987); English transl in: Russ. Math. Surv. 42, P. 127-168 (1987).B.S.Pavlov. Operator extensions theory and explicitly solvable models. Uspekhi Mat. Nauk. 42 (6). P. 99-131 (1987); English transl in: Russ. Math. Surv. 42, P. 127-168 (1987).N.Bagraev, G.Martin, B.S.Pavlov, A.Yafyasov. Landau-Zener effect for a quasi-2D periodic sandwich. Nanosystems: Phys. Chem. Math. 2 (4), P. 32-50 (2011).N.Bagraev, G.Martin, B.S.Pavlov, A.Yafyasov. Landau-Zener effect for a quasi-2D periodic sandwich. Nanosystems: Phys. Chem. Math. 2 (4), P. 32-50 (2011).V.Ryzhov. A general boundary value problem and its Weyl function. Opuscula Math. 27 (2), P. 305-331.V.Ryzhov. A general boundary value problem and its Weyl function. Opuscula Math. 27 (2), P. 305-331.M. Malamud, H. Neidhardt. Sturm-liouville boundary value problems with operator potentials and unitary equivalence. J. Differ. Equations, 252 (11), P. 5875–5922 (2012).M. Malamud, H. Neidhardt. Sturm-liouville boundary value problems with operator potentials and unitary equivalence. J. Differ. Equations, 252 (11), P. 5875–5922 (2012).V. I. Gorbachuk, M. L. Gorbachuk. Boundary value problems for operator differential equations, volume 48 of Mathematics and its Applications (Soviet Series). Kluwer Academic Publishers Group, Dordrecht (1991).V. I. Gorbachuk, M. L. Gorbachuk. Boundary value problems for operator differential equations, volume 48 of Mathematics and its Applications (Soviet Series). Kluwer Academic Publishers Group, Dordrecht (1991).V. A. Derkach and M. M. Malamud. Generalized resolvents and the boundary value problems for Hermitian operators with gaps. J. Funct. Anal. 95 (1), P. 1–95 (1991).V. A. Derkach and M. M. Malamud. Generalized resolvents and the boundary value problems for Hermitian operators with gaps. J. Funct. Anal. 95 (1), P. 1–95 (1991).M. M. Malamud. Some classes of extensions of a Hermitian operator with lacunae. Ukra¨ın. Mat. Zh. 44 (2), P. 215–233 (1992).M. M. Malamud. Some classes of extensions of a Hermitian operator with lacunae. Ukra¨ın. Mat. Zh. 44 (2), P. 215–233 (1992).H. Baumg¨artel, M. Wollenberg. Mathematical scattering theory, volume 59 of Mathematical Textbooks and Monographs, Part II: Mathematical Monographs. Akademie-Verlag, Berlin (1983).H. Baumg¨artel, M. Wollenberg. Mathematical scattering theory, volume 59 of Mathematical Textbooks and Monographs, Part II: Mathematical Monographs. Akademie-Verlag, Berlin (1983).V. A. Derkach, M. M. Malamud. On the Weyl function and Hermite operators with lacunae. Dokl. Akad. Nauk SSSR, 293 (5), P. 1041–1046 (1987).V. A. Derkach, M. M. Malamud. On the Weyl function and Hermite operators with lacunae. Dokl. Akad. Nauk SSSR, 293 (5), P. 1041–1046 (1987).V. A. Derkach, M. M. Malamud. The extension theory of Hermitian operators and the moment problem. J. Math. Sci. 73 (2), P. 141–242 (1995).V. A. Derkach, M. M. Malamud. The extension theory of Hermitian operators and the moment problem. J. Math. Sci. 73 (2), P. 141–242 (1995).J. Berndt, M. M. Malamud, H. Ntidhardt. Scattering matrices and Weyl functions. Proc. London Math. Soc. 97 (3), P. 568–598 (2008).J. Berndt, M. M. Malamud, H. Ntidhardt. Scattering matrices and Weyl functions. Proc. London Math. Soc. 97 (3), P. 568–598 (2008).A. N. Kochubei. On extensions of symmetric operators and symmetric binary relations. Mat. Zametki. 17, P. 41-48 (1975).A. N. Kochubei. On extensions of symmetric operators and symmetric binary relations. Mat. Zametki. 17, P. 41-48 (1975).

The authors declare that there are no conflicts of interest present.