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Algebra i Analiz, 2000, Volume 12, Issue 6, Pages 140–177 (Mi aa1132)  

This article is cited in 35 scientific papers (total in 35 papers)

Research Papers

Absolute continuity of the two-dimensional Schrödinger operator with delta potential concentrated on a periodic system of curves

M. Sh. Birman, T. A. Suslina, R. G. Shterenberg

St. Petersburg State University, Faculty of Physics
Received: 23.08.2000
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. Sh. Birman, T. A. Suslina, R. G. Shterenberg, “Absolute continuity of the two-dimensional Schrödinger operator with delta potential concentrated on a periodic system of curves”, Algebra i Analiz, 12:6 (2000), 140–177; St. Petersburg Math. J., 12:6 (2001), 983–1012
Citation in format AMSBIB
\Bibitem{BirSusSht00}
\by M.~Sh.~Birman, T.~A.~Suslina, R.~G.~Shterenberg
\paper Absolute continuity of the two-dimensional Schr\"odinger operator with delta potential concentrated on a periodic system of curves
\jour Algebra i Analiz
\yr 2000
\vol 12
\issue 6
\pages 140--177
\mathnet{http://mi.mathnet.ru/aa1132}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1816514}
\zmath{https://zbmath.org/?q=an:0998.35006}
\transl
\jour St. Petersburg Math. J.
\yr 2001
\vol 12
\issue 6
\pages 983--1012
Linking options:
  • https://www.mathnet.ru/eng/aa1132
  • https://www.mathnet.ru/eng/aa/v12/i6/p140
  • This publication is cited in the following 35 articles:
    1. Rabinovich V., “Magnetic Schrodinger Operators With Delta-Type Potentials”, Math. Meth. Appl. Sci., 44:12 (2021), 9746–9764  crossref  isi  scopus
    2. Rabinovich V., “Schrodinger Operators With Interactions on Unbounded Hypersurfaces”, Math. Meth. Appl. Sci., 42:15, SI (2019), 4981–4998  crossref  mathscinet  isi  scopus
    3. Barrera-Figueroa V., Rabinovich V.S., “Numerical Calculation of the Discrete Spectra of One-Dimensional Schrodinger Operators With Point Interactions”, Math. Meth. Appl. Sci., 42:15, SI (2019), 5072–5093  crossref  mathscinet  isi  scopus
    4. Rabinovich V., “Essential Spectrum of Schrodinger Operators With Delta and Delta `-Interactions on Systems of Unbounded Smooth Hypersurfaces in R-N”, Differential Equations, Mathematical Physics, and Applications: Selim Grigorievich Krein Centennial, Contemporary Mathematics, 734, eds. Kuchment P., Semenov E., Amer Mathematical Soc, 2019, 293–310  crossref  mathscinet  isi  scopus
    5. L. I. Danilov, “O spektre dvumernogo operatora Shredingera s odnorodnym magnitnym polem i periodicheskim elektricheskim potentsialom”, Izv. IMI UdGU, 51 (2018), 3–41  mathnet  crossref  elib
    6. D. I. Borisov, M. Znojil, “On eigenvalues of a PT-symmetric operator in a thin layer”, Sb. Math., 208:2 (2017), 173–199  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. Behrndt J., Frank R.L., Kuehn Ch., Lotoreichik V., Rohleder J., “Spectral Theory for Schrödinger Operators with
      \varvecδ
      -Interactions Supported on Curves in
      \varvecR3
      R 3”, Ann. Henri Poincare, 18:4 (2017), 1305–1347  crossref  mathscinet  zmath  isi  scopus
    8. V. S. Rabinovich, “Essential Spectrum of Schrödinger Operators with δ-Interactions on Unbounded Hypersurfaces”, Math. Notes, 102:5 (2017), 698–709  mathnet  crossref  crossref  mathscinet  isi  elib
    9. Mantile A., Posilicano A., Sini M., “Self-adjoint elliptic operators with boundary conditions on not closed hypersurfaces”, J. Differ. Equ., 261:1 (2016), 1–55  crossref  mathscinet  zmath  isi  elib  scopus
    10. Kuchment P., “An overview of periodic elliptic operators”, Bull. Amer. Math. Soc., 53:3 (2016), 343–414  crossref  mathscinet  zmath  isi  elib  scopus
    11. Dimassi M., “Semi-classical Asymptotics for Schrödinger Operator with Oscillating Decaying Potential”, Can. Math. Bul.-Bul. Can. Math., 59:4 (2016), 734–747  crossref  mathscinet  zmath  isi  scopus
    12. Exner P. Kovarik H., Quantum Waveguides, Theoretical and Mathematical Physics, Springer-Verlag Berlin, 2015, 1–382  crossref  mathscinet  isi
    13. L. I. Danilov, “O spektre dvumernogo obobschennogo periodicheskogo operatora Shredingera. II”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2014, no. 2, 3–28  mathnet
    14. L. I. Danilov, “O spektre dvumernogo obobschennogo periodicheskogo operatora Shredingera”, Izv. IMI UdGU, 2013, no. 1(41), 78–95  mathnet
    15. I. Kachkovskii, “Absence of Eigenvalues for the Periodic Schrödinger Operator with Singular Potential in a Rectangular Cylinder”, Funct. Anal. Appl., 47:2 (2013), 104–112  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    16. Behrndt J., Langer M., Lotoreichik V., “Schrodinger Operators with Delta and Delta `-Potentials Supported on Hypersurfaces”, Ann. Henri Poincare, 14:2 (2013), 385–423  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    17. I. Kachkovskiǐ, “Stein–Tomas theorem for a torus and the periodic Schrödinger operator with singular potential”, St. Petersburg Math. J., 24:6 (2013), 939–948  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    18. M. Z. Solomyak, T. A. Suslina, D. R. Yafaev, “On the mathematical works of M. Sh. Birman”, St. Petersburg Math. J., 23:1 (2012), 1–38  mathnet  crossref  mathscinet  zmath  isi  elib
    19. Danilov L.I., “On absolute continuity of the spectrum of a periodic magnetic Schrödinger operator”, J. Phys. A, 42:27 (2009), 275204, 20 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    20. Shen Zhongwei, Zhao Peihao, “Uniform Sobolev inequalities and absolute continuity of periodic operators”, Trans. Amer. Math. Soc., 360:4 (2008), 1741–1758  crossref  mathscinet  zmath  isi  elib  scopus
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