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Matrix Schrödinger operator with δ-interactions

Abstract

The matrix Schrödinger operator with point interactions on the semiaxis is studied. Using the theory of boundary triplets and the corresponding Weyl functions, we establish a relationship between the spectral properties (deficiency indices, self-adjointness, semiboundedness, etc.) of the operators under study and block Jacobi matrices of certain class.

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Correspondence to A. S. Kostenko.

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Original Russian Text © A. S. Kostenko, M. M. Malamud, D. D. Natyagailo, 2016, published in Matematicheskie Zametki, 2016, Vol. 100, No. 1, pp. 59–77.

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Kostenko, A.S., Malamud, M.M. & Natyagailo, D.D. Matrix Schrödinger operator with δ-interactions. Math Notes 100, 49–65 (2016). https://doi.org/10.1134/S0001434616070051

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  • DOI: https://doi.org/10.1134/S0001434616070051

Keywords

  • Schrödinger operator
  • Jacobi matrix
  • delta-interaction
  • self-adjointness
  • deficiency index