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Mat. Zametki, 2004, Volume 76, Issue 3, Pages 335–343 (Mi mz107)  

This article is cited in 2 scientific papers (total in 2 papers)

On Self-Adjoint Extensions of Schrödinger Operators Degenerating on a Pair of Half-Lines and the Corresponding Markovian Cocycles

G. G. Amosov, V. Zh. Sakbaev

Moscow Institute of Physics and Technology

Abstract: We consider the Schrödinger equation for a quantum particle whose mass depends on the position of the particle on the real line. The well-posedness of the Cauchy problem is studied for the Schrödinger equation with characteristic form degenerating outside the finite segment $I=[-l,l]\subset\mathbb R$. We show that this problem generates a unitary Markovian cocycle.

DOI: https://doi.org/10.4213/mzm107

Full text: PDF file (231 kB)
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English version:
Mathematical Notes, 2004, 76:3, 315–322

Bibliographic databases:

UDC: 517.958
Received: 18.11.2002
Revised: 01.04.2004

Citation: G. G. Amosov, V. Zh. Sakbaev, “On Self-Adjoint Extensions of Schrödinger Operators Degenerating on a Pair of Half-Lines and the Corresponding Markovian Cocycles”, Mat. Zametki, 76:3 (2004), 335–343; Math. Notes, 76:3 (2004), 315–322

Citation in format AMSBIB
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\by G.~G.~Amosov, V.~Zh.~Sakbaev
\paper On Self-Adjoint Extensions of Schrödinger Operators Degenerating on a~Pair of Half-Lines and the Corresponding Markovian Cocycles
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\pages 335--343
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. Zh. Sakbaev, “On the Cauchy problem for the Schrödinger equation degenerating outside a segment: properties of solutions and spectral aspects of the regularization”, Journal of Mathematical Sciences, 153:5 (2008), 562–590  mathnet  crossref  mathscinet  zmath
    2. V. Zh. Sakbaev, “Cauchy problem for degenerating linear differential equations and averaging of approximating regularizations”, Journal of Mathematical Sciences, 213:3 (2016), 287–459  mathnet  crossref  mathscinet
  • Математические заметки Mathematical Notes
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