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Zeroes of the Spectral Density of Discrete Schrödinger Operator with Wigner-von Neumann Potential. / Simonov, Sergey.

в: Integral Equations and Operator Theory, Том 73, № 3, 07.2012, стр. 351-364.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Simonov, S 2012, 'Zeroes of the Spectral Density of Discrete Schrödinger Operator with Wigner-von Neumann Potential', Integral Equations and Operator Theory, Том. 73, № 3, стр. 351-364. https://doi.org/10.1007/s00020-012-1972-x

APA

Simonov, S. (2012). Zeroes of the Spectral Density of Discrete Schrödinger Operator with Wigner-von Neumann Potential. Integral Equations and Operator Theory, 73(3), 351-364. https://doi.org/10.1007/s00020-012-1972-x

Vancouver

Simonov S. Zeroes of the Spectral Density of Discrete Schrödinger Operator with Wigner-von Neumann Potential. Integral Equations and Operator Theory. 2012 Июль;73(3):351-364. https://doi.org/10.1007/s00020-012-1972-x

Author

Simonov, Sergey. / Zeroes of the Spectral Density of Discrete Schrödinger Operator with Wigner-von Neumann Potential. в: Integral Equations and Operator Theory. 2012 ; Том 73, № 3. стр. 351-364.

BibTeX

@article{4e2e1cb88730433daa0407a2299dfb8c,
title = "Zeroes of the Spectral Density of Discrete Schr{\"o}dinger Operator with Wigner-von Neumann Potential",
abstract = "We consider a discrete Schr{\"o}dinger operator J whose potential is the sum of a Wigner-von Neumann term c sin(2ωn+δ)/n and a summable term. The essential spectrum of the operator J is equal to the interval [-2, 2]. Inside this interval, there are two critical points ±2 where eigenvalues may be situated. We prove that, generically, the spectral density of J has zeroes of the power {pipe}c{pipe}/2{pipe}sin ω{pipe} at these points.",
keywords = "Asymptotics of generalized eigenvectors, discrete Schr{\"o}dinger operator, Jacobi matrices, orthogonal polynomials, pseudogaps, Wigner-von Neumann potential",
author = "Sergey Simonov",
year = "2012",
month = jul,
doi = "10.1007/s00020-012-1972-x",
language = "English",
volume = "73",
pages = "351--364",
journal = "Integral Equations and Operator Theory",
issn = "0378-620X",
publisher = "Birkh{\"a}user Verlag AG",
number = "3",

}

RIS

TY - JOUR

T1 - Zeroes of the Spectral Density of Discrete Schrödinger Operator with Wigner-von Neumann Potential

AU - Simonov, Sergey

PY - 2012/7

Y1 - 2012/7

N2 - We consider a discrete Schrödinger operator J whose potential is the sum of a Wigner-von Neumann term c sin(2ωn+δ)/n and a summable term. The essential spectrum of the operator J is equal to the interval [-2, 2]. Inside this interval, there are two critical points ±2 where eigenvalues may be situated. We prove that, generically, the spectral density of J has zeroes of the power {pipe}c{pipe}/2{pipe}sin ω{pipe} at these points.

AB - We consider a discrete Schrödinger operator J whose potential is the sum of a Wigner-von Neumann term c sin(2ωn+δ)/n and a summable term. The essential spectrum of the operator J is equal to the interval [-2, 2]. Inside this interval, there are two critical points ±2 where eigenvalues may be situated. We prove that, generically, the spectral density of J has zeroes of the power {pipe}c{pipe}/2{pipe}sin ω{pipe} at these points.

KW - Asymptotics of generalized eigenvectors

KW - discrete Schrödinger operator

KW - Jacobi matrices

KW - orthogonal polynomials

KW - pseudogaps

KW - Wigner-von Neumann potential

UR - http://www.scopus.com/inward/record.url?scp=84864338528&partnerID=8YFLogxK

U2 - 10.1007/s00020-012-1972-x

DO - 10.1007/s00020-012-1972-x

M3 - Article

AN - SCOPUS:84864338528

VL - 73

SP - 351

EP - 364

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 3

ER -

ID: 9366517