Discrete spectrum of a periodic Schrödinger operator with variable metric perturbed by a nonnegative rapidly decaying potential

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Discrete spectrum of a periodic Schrödinger operator with variable metric perturbed by a nonnegative rapidly decaying potential. / Sloushch, V. A.

In: St. Petersburg Mathematical Journal, Vol. 27, No. 2, 2016, p. 317-326.

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

BibTeX

@article{74401de14bc546beb1df98a19682bbe2,

title = "Discrete spectrum of a periodic Schr{\"o}dinger operator with variable metric perturbed by a nonnegative rapidly decaying potential",

abstract = "The discrete spectrum is investigated that emerges in spectral gaps of the elliptic periodic operator $ A=-\mathrm {div} a(x)\mathrm {grad} +b(x)$, $ x\in \mathbb{R}^{d}$, perturbed by a nonnegative, ``rapidly'' decaying potential $\displaystyle 0\le V(x)\sim v(x/\vert x\vert)\vert x\vert^{-\varrho }, \quad \vert x\vert\to +\infty ,\quad \varrho \ge d. $ The asymptotics of the number of eigenvalues for the perturbed operator $ B(t)=A+tV$, $ t>0$, that have crossed a fixed point of the gap, is established with respect to the large coupling constant $ t$. - See more at: http://www.ams.org/journals/spmj/2016-27-02/S1061-0022-2016-01388-0/#Abstract",

keywords = "Periodic Schr\{"}odinger operator, discrete spectrum, spectral gap, asymptotics with respect to a large coupling constant, Cwikel-type estimate. - See more at: http://www.ams.org/journals/spmj/2016-27-02/S1061-0022-2016-01388-0/#sthash.6w99xYJK.dpuf",

author = "Sloushch, {V. A.}",

year = "2016",

doi = "http://dx.doi.org/10.1090/spmj/1388",

language = "не определен",

volume = "27",

pages = "317--326",

journal = "St. Petersburg Mathematical Journal",

issn = "1061-0022",

publisher = "American Mathematical Society",

number = "2",

}

RIS

TY - JOUR

T1 - Discrete spectrum of a periodic Schrödinger operator with variable metric perturbed by a nonnegative rapidly decaying potential

AU - Sloushch, V. A.

PY - 2016

Y1 - 2016

N2 - The discrete spectrum is investigated that emerges in spectral gaps of the elliptic periodic operator $ A=-\mathrm {div} a(x)\mathrm {grad} +b(x)$, $ x\in \mathbb{R}^{d}$, perturbed by a nonnegative, ``rapidly'' decaying potential $\displaystyle 0\le V(x)\sim v(x/\vert x\vert)\vert x\vert^{-\varrho }, \quad \vert x\vert\to +\infty ,\quad \varrho \ge d. $ The asymptotics of the number of eigenvalues for the perturbed operator $ B(t)=A+tV$, $ t>0$, that have crossed a fixed point of the gap, is established with respect to the large coupling constant $ t$. - See more at: http://www.ams.org/journals/spmj/2016-27-02/S1061-0022-2016-01388-0/#Abstract

AB - The discrete spectrum is investigated that emerges in spectral gaps of the elliptic periodic operator $ A=-\mathrm {div} a(x)\mathrm {grad} +b(x)$, $ x\in \mathbb{R}^{d}$, perturbed by a nonnegative, ``rapidly'' decaying potential $\displaystyle 0\le V(x)\sim v(x/\vert x\vert)\vert x\vert^{-\varrho }, \quad \vert x\vert\to +\infty ,\quad \varrho \ge d. $ The asymptotics of the number of eigenvalues for the perturbed operator $ B(t)=A+tV$, $ t>0$, that have crossed a fixed point of the gap, is established with respect to the large coupling constant $ t$. - See more at: http://www.ams.org/journals/spmj/2016-27-02/S1061-0022-2016-01388-0/#Abstract

KW - Periodic Schr\"odinger operator

KW - discrete spectrum

KW - spectral gap

KW - asymptotics with respect to a large coupling constant

KW - Cwikel-type estimate. - See more at: http://www.ams.org/journals/spmj/2016-27-02/S1061-0022-2016-01388-0/#sthash.6w99xYJK.dpuf

U2 - http://dx.doi.org/10.1090/spmj/1388

DO - http://dx.doi.org/10.1090/spmj/1388

M3 - статья

VL - 27

SP - 317

EP - 326

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 2

ER -

ID: 7557906