najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2017-8-2-166-179najo-648Research ArticleMATHEMATICSМАТЕМАТИКАCoupling of definitizable operators in Kreın spacesDerkachV.

Department of Mathematics; Department of Mathematics

Pirogova 9, Kiev, 01601; 600-Richchya Str 21, Vinnytsya, 21021

derkach.v@gmail.comTrunkC.

Postfach 100565, D-98684 Ilmenau

carsten.trunk@tu-ilmenau.deDragomanov National Pedagogical University; Vasyl Stus Donetsk National UniversityUkraineInstitut fur Mathematik, Technische Universitat IlmenauGermany20171208202582166179Copyright © Derkach V., Trunk C., 20252025Derkach V., Trunk C.Derkach V., Trunk C.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/648

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.

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