Coupling of definitizable operators in Kreın spaces
https://doi.org/10.17586/2220-8054-2017-8-2-166-179
Abstract
Indefinite Sturm–Liouville operators defined on R are often considered as a coupling of two semibounded symmetric operators defined on R + and R −, respectively. In many situations, those two semibounded symmetric operators have in a special sense good properties like a Hilbert space self-adjoint extension.
In this paper, we present an abstract approach to the coupling of two (definitizable) self-adjoint operators. We obtain a characterization for the definitizability and the regularity of the critical points. Finally we study a typical class of indefinite Sturm–Liouville problems on R.
Keywords
self-adjoint extension,
symmetric operator,
Kreın space,
locally definitizable operator,
coupling of operators,
boundary triple,
Weyl function,
regular critical point
Supporting agencies: The research of the first author was supported by the Deutsche Forschungsgemeinschaft (DFG) under grant no. TR 903/16-1 and Ministry of Education and Science of Ukraine (projects # 0115U000136, 0115U000556.
About the Authors
V. Derkach
Dragomanov National Pedagogical University; Vasyl Stus Donetsk National University
Ukraine
Ukraine
Department of Mathematics; Department of Mathematics
Pirogova 9, Kiev, 01601; 600-Richchya Str 21, Vinnytsya, 21021
C. Trunk
Institut fur Mathematik, Technische Universitat Ilmenau
Germany
Germany
Postfach 100565, D-98684 Ilmenau
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Review
For citations:
Derkach V., Trunk C. Coupling of definitizable operators in Kreın spaces. Nanosystems: Physics, Chemistry, Mathematics. 2017;8(2):166-179. https://doi.org/10.17586/2220-8054-2017-8-2-166-179
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