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The discrete spectrum of cross-shaped waveguides. / Bakharev, F. L.; Matveenko, S. G.; Nazarov, S. A.

In: St. Petersburg Mathematical Journal, Vol. 28, No. 2, 01.01.2017, p. 171-180.

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

Harvard

Bakharev, FL, Matveenko, SG & Nazarov, SA 2017, 'The discrete spectrum of cross-shaped waveguides', St. Petersburg Mathematical Journal, vol. 28, no. 2, pp. 171-180. https://doi.org/10.1090/spmj/1444

APA

Bakharev, F. L., Matveenko, S. G., & Nazarov, S. A. (2017). The discrete spectrum of cross-shaped waveguides. St. Petersburg Mathematical Journal, 28(2), 171-180. https://doi.org/10.1090/spmj/1444

Vancouver

Bakharev FL, Matveenko SG, Nazarov SA. The discrete spectrum of cross-shaped waveguides. St. Petersburg Mathematical Journal. 2017 Jan 1;28(2):171-180. https://doi.org/10.1090/spmj/1444

Author

Bakharev, F. L. ; Matveenko, S. G. ; Nazarov, S. A. / The discrete spectrum of cross-shaped waveguides. In: St. Petersburg Mathematical Journal. 2017 ; Vol. 28, No. 2. pp. 171-180.

BibTeX

@article{b8800213c96944f4948be94808bf9afa,
title = "The discrete spectrum of cross-shaped waveguides",
abstract = "The discrete spectrum of the Dirichlet problem for the Laplace operator on the union of two circular unit cylinders whose axes intersect at the right angle consists of a single eigenvalue. For the threshold value of the spectral parameter, this problem has no bounded solutions. When the angle between the axes reduces, the multiplicity of the discrete spectrum grows unboundedly.",
keywords = "Cross-shaped quantum waveguide, Discrete spectrum multiplicity, Stabilizing solution at the threshold of the continuous spectrum",
author = "Bakharev, {F. L.} and Matveenko, {S. G.} and Nazarov, {S. A.}",
year = "2017",
month = jan,
day = "1",
doi = "10.1090/spmj/1444",
language = "English",
volume = "28",
pages = "171--180",
journal = "St. Petersburg Mathematical Journal",
issn = "1061-0022",
publisher = "American Mathematical Society",
number = "2",

}

RIS

TY - JOUR

T1 - The discrete spectrum of cross-shaped waveguides

AU - Bakharev, F. L.

AU - Matveenko, S. G.

AU - Nazarov, S. A.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - The discrete spectrum of the Dirichlet problem for the Laplace operator on the union of two circular unit cylinders whose axes intersect at the right angle consists of a single eigenvalue. For the threshold value of the spectral parameter, this problem has no bounded solutions. When the angle between the axes reduces, the multiplicity of the discrete spectrum grows unboundedly.

AB - The discrete spectrum of the Dirichlet problem for the Laplace operator on the union of two circular unit cylinders whose axes intersect at the right angle consists of a single eigenvalue. For the threshold value of the spectral parameter, this problem has no bounded solutions. When the angle between the axes reduces, the multiplicity of the discrete spectrum grows unboundedly.

KW - Cross-shaped quantum waveguide

KW - Discrete spectrum multiplicity

KW - Stabilizing solution at the threshold of the continuous spectrum

UR - http://www.scopus.com/inward/record.url?scp=85013399413&partnerID=8YFLogxK

UR - https://www.elibrary.ru/item.asp?id=29480946

U2 - 10.1090/spmj/1444

DO - 10.1090/spmj/1444

M3 - Article

AN - SCOPUS:85013399413

VL - 28

SP - 171

EP - 180

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 2

ER -

ID: 34905699