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Funktsional. Anal. i Prilozhen., 2014, Volume 48, Issue 4, Pages 74–77 (Mi faa3157)  

This article is cited in 4 scientific papers (total in 4 papers)

Brief communications

Two-Dimensional von Neumann–Wigner Potentials with a Multiple Positive Eigenvalue

R. G. Novikova, I. A. Taimanovbc, S. P. Tsarevd

a École Polytechnique, Centre de Mathématiques Appliquées
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
c Novosibirsk State University
d Institute of Space and Information Technologies, Siberian Federal University

Abstract: By the Moutard transformation method we construct two-dimensional Schrödinger operators with real smooth potentials decaying at infinity and having a multiple positive eigenvalue. These potentials are rational functions of spatial variables and their sines and cosines.

Keywords: two-dimensional Schrödinger operator, Moutard transformation, positive eigenvalues

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.A18.21.0866
1.1462.2014/К
Ministry of Education and Science of the Republic of Kazakhstan 1431/ГФ


DOI: https://doi.org/10.4213/faa3157

Full text: PDF file (159 kB)
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English version:
Functional Analysis and Its Applications, 2014, 48:4, 295–297

Bibliographic databases:

UDC: 517.95+517.984.5
Received: 02.08.2013

Citation: R. G. Novikov, I. A. Taimanov, S. P. Tsarev, “Two-Dimensional von Neumann–Wigner Potentials with a Multiple Positive Eigenvalue”, Funktsional. Anal. i Prilozhen., 48:4 (2014), 74–77; Funct. Anal. Appl., 48:4 (2014), 295–297

Citation in format AMSBIB
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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. P. G. Grinevich, R. G. Novikov, “Moutard transform for generalized analytic functions”, J. Geom. Anal., 26:4 (2016), 2984–2995  crossref  mathscinet  zmath  isi  scopus
    2. P. G. Grinevich, R. G. Novikov, “Moutard transform approach to generalized analytic functions with contour poles”, Bull. Sci. Math., 140:6 (2016), 638–656  crossref  mathscinet  zmath  isi  elib  scopus
    3. J. Lorinczi, I. Sasaki, “Embedded eigenvalues and Neumann-Wigner potentials for relativistic Schrödinger operators”, J. Funct. Anal., 273:4 (2017), 1548–1575  crossref  mathscinet  zmath  isi  scopus
    4. R. G. Novikov, I. A. Taimanov, “Darboux–Moutard transformations and Poincaré–Steklov operators”, Proc. Steklov Inst. Math., 302 (2018), 315–324  mathnet  crossref  crossref  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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