Inverse resonance scattering on rotationally symmetric manifolds

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Inverse resonance scattering on rotationally symmetric manifolds. / Isozaki, Hiroshi; Korotyaev, Evgeny.

In: Asymptotic Analysis, Vol. 125, No. 3-4, 2021, p. 347-363.

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

Author

Isozaki, Hiroshi ; Korotyaev, Evgeny. / Inverse resonance scattering on rotationally symmetric manifolds. In: Asymptotic Analysis. 2021 ; Vol. 125, No. 3-4. pp. 347-363.

BibTeX

@article{6ccbc685a26c46fd9353dfb27dbf80cb,

title = "Inverse resonance scattering on rotationally symmetric manifolds",

abstract = "We discuss inverse resonance scattering for the Laplacian on a rotationally symmetric manifold M = ( 0 , ∞ ) × Y whose rotation radius is constant outside some compact interval. The Laplacian on M is unitarily equivalent to a direct sum of one-dimensional Schrodinger operators with compactly supported potentials on the half-line. We prove Asymptotics of counting function of resonances at large radius. The rotation radius is uniquely determined by its eigenvalues and resonances. There exists an algorithm to recover the rotation radius from its eigenvalues and resonances. The proof is based on some non-linear real analytic isomorphism between two Hilbert spaces. ",

keywords = "Inverse resonance scattering, iso-resonance sets, rotationally symmetric manifolds, SPECTRAL ASYMPTOTICS, BOUNDS, REVOLUTION, TERMS, POLES, LAPLACE OPERATOR, SURFACES",

author = "Hiroshi Isozaki and Evgeny Korotyaev",

year = "2021",

doi = "10.3233/ASY-201659",

language = "English",

volume = "125",

pages = "347--363",

journal = "Asymptotic Analysis",

issn = "0921-7134",

publisher = "IOS Press",

number = "3-4",

}

RIS

TY - JOUR

T1 - Inverse resonance scattering on rotationally symmetric manifolds

AU - Isozaki, Hiroshi

AU - Korotyaev, Evgeny

PY - 2021

Y1 - 2021

N2 - We discuss inverse resonance scattering for the Laplacian on a rotationally symmetric manifold M = ( 0 , ∞ ) × Y whose rotation radius is constant outside some compact interval. The Laplacian on M is unitarily equivalent to a direct sum of one-dimensional Schrodinger operators with compactly supported potentials on the half-line. We prove Asymptotics of counting function of resonances at large radius. The rotation radius is uniquely determined by its eigenvalues and resonances. There exists an algorithm to recover the rotation radius from its eigenvalues and resonances. The proof is based on some non-linear real analytic isomorphism between two Hilbert spaces.

AB - We discuss inverse resonance scattering for the Laplacian on a rotationally symmetric manifold M = ( 0 , ∞ ) × Y whose rotation radius is constant outside some compact interval. The Laplacian on M is unitarily equivalent to a direct sum of one-dimensional Schrodinger operators with compactly supported potentials on the half-line. We prove Asymptotics of counting function of resonances at large radius. The rotation radius is uniquely determined by its eigenvalues and resonances. There exists an algorithm to recover the rotation radius from its eigenvalues and resonances. The proof is based on some non-linear real analytic isomorphism between two Hilbert spaces.

KW - Inverse resonance scattering

KW - iso-resonance sets

KW - rotationally symmetric manifolds

KW - SPECTRAL ASYMPTOTICS

KW - BOUNDS

KW - REVOLUTION

KW - TERMS

KW - POLES

KW - LAPLACE OPERATOR

KW - SURFACES

UR - http://www.scopus.com/inward/record.url?scp=85117941272&partnerID=8YFLogxK

U2 - 10.3233/ASY-201659

DO - 10.3233/ASY-201659

M3 - Article

AN - SCOPUS:85117941272

VL - 125

SP - 347

EP - 363

JO - Asymptotic Analysis

JF - Asymptotic Analysis

SN - 0921-7134

IS - 3-4

ER -

ID: 88200033