Behavior of waveguide scattering matrices in a neighborhood of thresholds

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Behavior of waveguide scattering matrices in a neighborhood of thresholds. / Plamenevskii, B. A.; Poretskii, A. S.

In: St. Petersburg Mathematical Journal, Vol. 30, No. 2, 2019, p. 285-319.

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

BibTeX

@article{521dfe243dd24bb79f9161b26f1bf6d0,

title = "Behavior of waveguide scattering matrices in a neighborhood of thresholds",

abstract = "A waveguide occupies a d+1-dimensional domain with several cylindrical outlets to infinity. The waveguide is described by a general elliptic boundary value problem with spectral parameter μ, selfadjoint with respect to the Green formula. At infinity, the coefficients of the problem stabilize at an exponential rate to functions independent of the axial variable in the corresponding cylinder. On every interval of the continuous spectrum between neighboring {"}thresholds{"}, a unitary scattering matrix S(μ) is defined; the size of S(μ) is finite for any μ, remains to be constant on any such interval, and varies from an interval to an interval. The basic result claims the existence of finite one-sided limits of the scattering matrix S(μ) at every threshold.",

keywords = "Analytic continuation, Dispersion relations, Elliptic problems, One-sided limits at thresholds, Stable basis of waves",

author = "Plamenevskii, {B. A.} and Poretskii, {A. S.}",

year = "2019",

doi = "10.1090/spmj/1543",

language = "English",

volume = "30",

pages = "285--319",

journal = "St. Petersburg Mathematical Journal",

issn = "1061-0022",

publisher = "American Mathematical Society",

number = "2",

}

RIS

TY - JOUR

T1 - Behavior of waveguide scattering matrices in a neighborhood of thresholds

AU - Plamenevskii, B. A.

AU - Poretskii, A. S.

PY - 2019

Y1 - 2019

N2 - A waveguide occupies a d+1-dimensional domain with several cylindrical outlets to infinity. The waveguide is described by a general elliptic boundary value problem with spectral parameter μ, selfadjoint with respect to the Green formula. At infinity, the coefficients of the problem stabilize at an exponential rate to functions independent of the axial variable in the corresponding cylinder. On every interval of the continuous spectrum between neighboring "thresholds", a unitary scattering matrix S(μ) is defined; the size of S(μ) is finite for any μ, remains to be constant on any such interval, and varies from an interval to an interval. The basic result claims the existence of finite one-sided limits of the scattering matrix S(μ) at every threshold.

AB - A waveguide occupies a d+1-dimensional domain with several cylindrical outlets to infinity. The waveguide is described by a general elliptic boundary value problem with spectral parameter μ, selfadjoint with respect to the Green formula. At infinity, the coefficients of the problem stabilize at an exponential rate to functions independent of the axial variable in the corresponding cylinder. On every interval of the continuous spectrum between neighboring "thresholds", a unitary scattering matrix S(μ) is defined; the size of S(μ) is finite for any μ, remains to be constant on any such interval, and varies from an interval to an interval. The basic result claims the existence of finite one-sided limits of the scattering matrix S(μ) at every threshold.

KW - Analytic continuation

KW - Dispersion relations

KW - Elliptic problems

KW - One-sided limits at thresholds

KW - Stable basis of waves

UR - http://www.scopus.com/inward/record.url?scp=85056271067&partnerID=8YFLogxK

U2 - 10.1090/spmj/1543

DO - 10.1090/spmj/1543

M3 - Article

AN - SCOPUS:85056271067

VL - 30

SP - 285

EP - 319

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 2

ER -

ID: 50415309