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Zap. Nauchn. Sem. POMI, 2000, Volume 271, Pages 276–312 (Mi znsl1359)  

This article is cited in 10 scientific papers (total in 10 papers)

Absolute continuity of a two-dimensional magnetic periodic Schrödinger operator with measure derivative like potential

R. G. Shterenberg

Saint-Petersburg State University

Abstract: A two-dimensional magnetic periodic Schrödinger operator with variable metric is considered. Electric potential is suggested to be a distribution formally given by the expression $\frac{d\nu}{d\bold x}$, where $d\nu$ is a periodic measure with locally finite variation. We assume that the perturbation generated by electric potential is strongly subordinate (in the sense of forms) to the free operator. Under this natural assumption, we prove the absolute continuity of the spectrum of the Schrödinger operator.

Full text: PDF file (358 kB)

English version:
Journal of Mathematical Sciences (New York), 2003, 115:6, 2862–2882

Bibliographic databases:

UDC: 517
Received: 23.10.2000

Citation: R. G. Shterenberg, “Absolute continuity of a two-dimensional magnetic periodic Schrödinger operator with measure derivative like potential”, Boundary-value problems of mathematical physics and related problems of function theory. Part 31, Zap. Nauchn. Sem. POMI, 271, POMI, St. Petersburg, 2000, 276–312; J. Math. Sci. (N. Y.), 115:6 (2003), 2862–2882

Citation in format AMSBIB
\Bibitem{Sht00}
\by R.~G.~Shterenberg
\paper Absolute continuity of a two-dimensional magnetic periodic Schr\"odinger operator with measure derivative like potential
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~31
\serial Zap. Nauchn. Sem. POMI
\yr 2000
\vol 271
\pages 276--312
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1359}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1810620}
\zmath{https://zbmath.org/?q=an:1040.35049}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2003
\vol 115
\issue 6
\pages 2862--2882
\crossref{https://doi.org/10.1023/A:1023334206109}


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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. Suslina T.A., “On the absence of eigenvalues of a periodic matrix Schrodinger operator in a layer”, Russian Journal of Mathematical Physics, 8:4 (2001), 463–486  mathscinet  zmath  isi
    2. L. I. Danilov, “The Spectrum of the Two-Dimensional Periodic Schrödinger Operator”, Theoret. and Math. Phys., 134:3 (2003), 392–403  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. R. G. Shterenberg, “Absolute continuity of the spectrum of two-dimensional periodic Schrödinger operators with strongly subordinate magnetic potential”, J. Math. Sci. (N. Y.), 129:4 (2005), 4087–4109  mathnet  crossref  mathscinet  zmath
    4. R. G. Shterenberg, “Schrödinger operator in a periodic waveguide on the plane and quasi-conformal mappings”, J. Math. Sci. (N. Y.), 127:2 (2005), 1936–1956  mathnet  crossref  mathscinet  zmath
    5. Shargorodsky E., Sobolev A.V., “Quasiconformal mappings and periodic spectral problems in dimension two”, Journal D Analyse Mathematique, 91 (2003), 67–103  crossref  mathscinet  zmath  isi  scopus
    6. L. I. Danilov, “Ob otsutstvii sobstvennykh znachenii v spektre dvumernykh periodicheskikh operatorov Diraka i Shredingera”, Izv. IMI UdGU, 2004, no. 1(29), 49–84  mathnet
    7. L. I. Danilov, “The absence of eigenvalues in the spectrum of ageneralized two-dimensional periodic Dirac operator”, St. Petersburg Math. J., 17:3 (2006), 409–433  mathnet  crossref  mathscinet  zmath
    8. Shen Zh., Zhao P., “Uniform Sobolev inequalities and absolute continuity of periodic operators”, Transactions of the American Mathematical Society, 360:4 (2008), 1741–1758  crossref  mathscinet  zmath  isi  scopus
    9. Danilov L.I., “On absolute continuity of the spectrum of a periodic magnetic Schrodinger operator”, Journal of Physics A-Mathematical and Theoretical, 42:27 (2009), 275204  crossref  mathscinet  zmath  adsnasa  isi  scopus
    10. 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
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