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Zap. Nauchn. Sem. POMI, 2004, Volume 318, Pages 298–307 (Mi znsl711)  

This article is cited in 18 scientific papers (total in 18 papers)

Absence of the singular continuous component in the spectrum of analytic direct integrals

N. Filonova, A. V. Sobolevb

a St. Petersburg State University, Faculty of Physics
b University of Sussex

Abstract: We give a simple proof of the absence of the singular continuous component in the spectrum of self-adjoint operators representable as analytic direct integrals.

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English version:
Journal of Mathematical Sciences (New York), 2006, 136:2, 3826–3831

Bibliographic databases:

UDC: 517
Received: 17.08.2004
Language:

Citation: N. Filonov, A. V. Sobolev, “Absence of the singular continuous component in the spectrum of analytic direct integrals”, Boundary-value problems of mathematical physics and related problems of function theory. Part 36, Zap. Nauchn. Sem. POMI, 318, POMI, St. Petersburg, 2004, 298–307; J. Math. Sci. (N. Y.), 136:2 (2006), 3826–3831

Citation in format AMSBIB
\Bibitem{FilSob04}
\by N.~Filonov, A.~V.~Sobolev
\paper Absence of the singular continuous component in the spectrum of analytic direct integrals
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~36
\serial Zap. Nauchn. Sem. POMI
\yr 2004
\vol 318
\pages 298--307
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl711}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2120804}
\zmath{https://zbmath.org/?q=an:1084.47021}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 136
\issue 2
\pages 3826--3831
\crossref{https://doi.org/10.1007/s10958-006-0203-x}


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    Citing articles on Google Scholar: Russian citations, English citations
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    1. Murata M., Tsuchida T., “Asymptotics of Green functions and the limiting absorption principle for elliptic operators with periodic coefficients”, J Math Kyoto Univ, 46:4 (2006), 713–754  crossref  mathscinet  zmath  isi  scopus
    2. L. I. Danilov, “Ob absolyutnoi nepreryvnosti spektra trekhmernogo periodicheskogo operatora Diraka”, Izv. IMI UdGU, 2006, no. 1(35), 49–76  mathnet
    3. Mantoiu M., Richard S., de Aldecoa R.T., “Spectral analysis for adjacency operators on graphs”, Ann Henri Poincaré, 8:7 (2007), 1401–1423  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. Frank R.L., Shterenberg R.G., “On the spectrum of partially periodic operators”, Operator Theory, Analysis and Mathematical Physics, Operator Theory : Advances and Applications, 174, 2007, 35–50  crossref  mathscinet  zmath  isi
    5. L. I. Danilov, “Absolyutnaya nepreryvnost spektra mnogomernogo periodicheskogo magnitnogo operatora Diraka”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2008, no. 1, 61–96  mathnet
    6. 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
    7. Hempel R., Kohlmann M., “A variational approach to dislocation problems for periodic Schrodinger operators”, J Math Anal Appl, 381:1 (2011), 166–178  crossref  mathscinet  zmath  isi  elib  scopus
    8. Danilov L.I., “On Absolute Continuity of the Spectrum of a 3D Periodic Magnetic Dirac Operator”, Integral Equations Operator Theory, 71:4 (2011), 535–556  crossref  mathscinet  zmath  isi  elib  scopus
    9. L. I. Danilov, “O spektre periodicheskogo operatora Shredingera s potentsialom iz prostranstva Morri”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2012, no. 3, 25–47  mathnet
    10. 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
    11. Filonov N.D., Sobolev A.V., “on the Spectrum of An “Even” Periodic Schrodinger Operator With a Rational Magnetic Flux”, J. Spectr. Theory, 5:2 (2015), 381–398  crossref  mathscinet  zmath  isi  elib  scopus
    12. L. I. Danilov, “O spektre periodicheskogo magnitnogo operatora Diraka”, Izv. IMI UdGU, 2016, no. 2(48), 3–21  mathnet  elib
    13. Kuchment P., “An overview of periodic elliptic operators”, Bull. Amer. Math. Soc., 53:3 (2016), 343–414  crossref  mathscinet  zmath  isi  elib  scopus
    14. N. Filonov, “Absolute continuity of 2D Schrödinger operator with partially periodic coefficients”, St. Petersburg Math. J., 29:2 (2018), 383–398  mathnet  crossref  mathscinet  isi  elib
    15. A. O. Prokhorov, N. D. Filonov, “The Maxwell operator with periodic coefficients in a cylinder”, St. Petersburg Math. J., 29:6 (2018), 997–1006  mathnet  crossref  mathscinet  isi  elib
    16. M. V. Platonova, K. S. Ryadovkin, “Branching random walks on $\mathbf{Z}^d$ with periodic branching sources”, Theory Probab. Appl., 64:2 (2019), 229–248  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    17. L. I. Danilov, “O spektre relyativistskogo gamiltoniana Landau s periodicheskim elektricheskim potentsialom”, Izv. IMI UdGU, 54 (2019), 3–26  mathnet  crossref
    18. N. D. Filonov, “Operator Maksvella v tsilindre s koeffitsientami, ne zavisyaschimi ot poperechnykh peremennykh”, Algebra i analiz, 32:1 (2020), 187–207  mathnet
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