Spectral determination of analytic bi-axisymmetric plane domains

Steve Zelditch

doi:10.4310/mrl.1999.v6.n4.a8

Spectral determination of analytic bi-axisymmetric plane domains

Steve Zelditch^*

^*Corresponding author for this work

Mathematics

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

5 Scopus citations

Abstract

Let D denote the class of bounded simply connected real analytic plane domains with the symmetry of an ellipse. We announce a proof that under generic assumptions, if Ω₁, Ω₂ ∈ D and if the Dirichlet spectra coincide, Spec(Ω₁) = Spec(Ω₂), then Ω₁ = Ω₂ up to rigid motion.

Original language	English (US)
Pages (from-to)	457-464
Number of pages	8
Journal	Mathematical Research Letters
Volume	6
Issue number	3-4
DOIs	https://doi.org/10.4310/mrl.1999.v6.n4.a8
State	Published - 1999

ASJC Scopus subject areas

General Mathematics

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10.4310/mrl.1999.v6.n4.a8

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title = "Spectral determination of analytic bi-axisymmetric plane domains",

abstract = "Let D denote the class of bounded simply connected real analytic plane domains with the symmetry of an ellipse. We announce a proof that under generic assumptions, if Ω1, Ω2 ∈ D and if the Dirichlet spectra coincide, Spec(Ω1) = Spec(Ω2), then Ω1 = Ω2 up to rigid motion.",

author = "Steve Zelditch",

year = "1999",

doi = "10.4310/mrl.1999.v6.n4.a8",

language = "English (US)",

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pages = "457--464",

journal = "Mathematical Research Letters",

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T1 - Spectral determination of analytic bi-axisymmetric plane domains

AU - Zelditch, Steve

PY - 1999

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N2 - Let D denote the class of bounded simply connected real analytic plane domains with the symmetry of an ellipse. We announce a proof that under generic assumptions, if Ω1, Ω2 ∈ D and if the Dirichlet spectra coincide, Spec(Ω1) = Spec(Ω2), then Ω1 = Ω2 up to rigid motion.

AB - Let D denote the class of bounded simply connected real analytic plane domains with the symmetry of an ellipse. We announce a proof that under generic assumptions, if Ω1, Ω2 ∈ D and if the Dirichlet spectra coincide, Spec(Ω1) = Spec(Ω2), then Ω1 = Ω2 up to rigid motion.

UR - https://www.scopus.com/pages/publications/0033245943

UR - https://www.scopus.com/inward/citedby.url?scp=0033245943&partnerID=8YFLogxK

U2 - 10.4310/mrl.1999.v6.n4.a8

DO - 10.4310/mrl.1999.v6.n4.a8

M3 - Article

AN - SCOPUS:0033245943

SN - 1073-2780

VL - 6

SP - 457

EP - 464

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 3-4

ER -

Spectral determination of analytic bi-axisymmetric plane domains

Abstract

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