Matrix Schrödinger Operator with $\delta$-Interactions

Kostenko, Aleksey; Malamud, M. M.; Natiagailo, Daria

doi:10.4213/mzm11122

Matematicheskie Zametki

2016

DOI: 10.4213/mzm11122

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Matrix Schrödinger Operator with $\delta$-Interactions

Aleksey Kostenko¹,

M. M. Malamud²,

Daria Natiagailo³

Abstract: Изучается матричный оператор Шрeдингера с точечными взаимодействиями на полуоси. Используя теорию граничных троек и соответствующих им функций Вейля, мы устанавливаем связь между спектральными свойствами (индексы дефекта, самосопряженность, полуограниченность и т.д.) исследуемых операторов и некоторого класса блочных якобиевых матриц. Библиография: 26 названий.

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Cited by 7 publications

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On the Deficiency Indices of Block Jacobi Matrices Related to Dirac Operators with Point Interactions

Budyka¹,

Malamud

2019

Math Notes

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The paper concerns with infinite block Jacobi matrices J with p × p-matrix entries. We present new conditions for these block matrices to be selfadjoint and have discrete spectrum. In our previous papers there was established a close relation between a class of such matrices and 2p × 2p Dirac operators with point interactions in L 2 (R; C 2p). For block Jacobi matrices J of this class we present several conditions ensuring either maximality or intermediatory of their deficiency indices. Applications to Dirac and matrix Schrodinger operators are given. It is worth mentioning that the above mentioned connection is employed here in both directions for the first time. In particular, the property of J to have maximal deficiency indices was firstly established for Dirac operators.

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On the Deficiency Indices of Block Jacobi Matrices Related to Dirac Operators with Point Interactions

Budyka¹,

Malamud

2019

Math Notes

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show abstract

Infinite quantum graphs

et al. 2017

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Об Индексах Дефекта Блочно Якобиевых Матриц, Связанных С Операторами Дирака С Точечными Взаимодействиями

Будыка¹,

Budyka

Malamud³

2019

Matematicheskie Zametki

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Matrix Schrödinger Operator with $\delta$-Interactions

Cited by 7 publications

References 16 publications

On the Deficiency Indices of Block Jacobi Matrices Related to Dirac Operators with Point Interactions

On the Deficiency Indices of Block Jacobi Matrices Related to Dirac Operators with Point Interactions

Infinite quantum graphs

Об Индексах Дефекта Блочно Якобиевых Матриц, Связанных С Операторами Дирака С Точечными Взаимодействиями

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