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A third order operator with periodic coefficients on the real line. / Badanin, A.V.; Korotyaev, E.L.

In: St. Petersburg Mathematical Journal, Vol. 25, No. 5, 2014, p. 713-734.

Research output: Contribution to journal › Article › peer-review

Harvard

Badanin, AV & Korotyaev, EL 2014, 'A third order operator with periodic coefficients on the real line', St. Petersburg Mathematical Journal, vol. 25, no. 5, pp. 713-734. <http://www.ams.org/journals/spmj/2014-25-05/S1061-0022-2014-01313-1/>

APA

Badanin, A. V., & Korotyaev, E. L. (2014). A third order operator with periodic coefficients on the real line. St. Petersburg Mathematical Journal, 25(5), 713-734. http://www.ams.org/journals/spmj/2014-25-05/S1061-0022-2014-01313-1/

Vancouver

Badanin AV, Korotyaev EL. A third order operator with periodic coefficients on the real line. St. Petersburg Mathematical Journal. 2014;25(5):713-734.

Author

Badanin, A.V. ; Korotyaev, E.L. / A third order operator with periodic coefficients on the real line. In: St. Petersburg Mathematical Journal. 2014 ; Vol. 25, No. 5. pp. 713-734.

BibTeX

@article{1e10c14af0b74a71b5a5b446eb3cfcc4,
title = "A third order operator with periodic coefficients on the real line",
abstract = "The operator i∂3+i∂p+ip∂+q with 1-periodic coefficients p, q ∈ L1 loc(R) is considered on the real line. The following results are obtained: 1) the spectrum of this operator is absolutely continuous, covers the entire real line, and has multiplicity one or three; 2) the spectrum of multiplicity three is bounded and expressed in terms of real zeros of a certain entire function; 3) the Lyapunov function, analytic on a 3-sheeted Riemann surface, is constructed and investigated.",
keywords = "Periodic third order operator, spectral bands, spectral asymptotics.",
author = "A.V. Badanin and E.L. Korotyaev",
year = "2014",
language = "English",
volume = "25",
pages = "713--734",
journal = "St. Petersburg Mathematical Journal",
issn = "1061-0022",
publisher = "American Mathematical Society",
number = "5",

}

RIS

TY - JOUR

T1 - A third order operator with periodic coefficients on the real line

AU - Badanin, A.V.

AU - Korotyaev, E.L.

PY - 2014

Y1 - 2014

N2 - The operator i∂3+i∂p+ip∂+q with 1-periodic coefficients p, q ∈ L1 loc(R) is considered on the real line. The following results are obtained: 1) the spectrum of this operator is absolutely continuous, covers the entire real line, and has multiplicity one or three; 2) the spectrum of multiplicity three is bounded and expressed in terms of real zeros of a certain entire function; 3) the Lyapunov function, analytic on a 3-sheeted Riemann surface, is constructed and investigated.

AB - The operator i∂3+i∂p+ip∂+q with 1-periodic coefficients p, q ∈ L1 loc(R) is considered on the real line. The following results are obtained: 1) the spectrum of this operator is absolutely continuous, covers the entire real line, and has multiplicity one or three; 2) the spectrum of multiplicity three is bounded and expressed in terms of real zeros of a certain entire function; 3) the Lyapunov function, analytic on a 3-sheeted Riemann surface, is constructed and investigated.

KW - Periodic third order operator

KW - spectral bands

KW - spectral asymptotics.

M3 - Article

VL - 25

SP - 713

EP - 734

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 5

ER -

ID: 7032998