• Title/Summary/Keyword: selfadjoint extensions

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Comparative Analysis of Spectral Theory of Second Order Difference and Differential Operators with Unbounded Odd Coefficient

  • Nyamwala, Fredrick Oluoch;Ambogo, David Otieno;Ngala, Joyce Mukhwana
    • Kyungpook Mathematical Journal
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    • v.60 no.2
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    • pp.297-305
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    • 2020
  • We show that selfadjoint operator extensions of minimal second order difference operators have only discrete spectrum when the odd order coefficient is unbounded but grows or decays according to specific conditions. Selfadjoint operator extensions of minimal differential operator under similar growth and decay conditions on the coefficients have a absolutely continuous spectrum of multiplicity one.

ON THE APPROXIMATION BY REGULAR POTENTIALS OF SCHRÖDINGER OPERATORS WITH POINT INTERACTIONS

  • Galtbayar, Artbazar;Yajima, Kenji
    • Journal of the Korean Mathematical Society
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    • v.57 no.2
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    • pp.429-450
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    • 2020
  • We prove that wave operators for Schrödinger operators with multi-center local point interactions are scaling limits of the ones for Schrödinger operators with regular potentials. We simultaneously present a proof of the corresponding well known result for the resolvent which substantially simplifies the one by Albeverio et al.