Spectral determination of analytic bi-axisymmetric plane domains

Steve Zelditch

doi:10.1007/PL00001633

Spectral determination of analytic bi-axisymmetric plane domains

Steve Zelditch^*

^*Corresponding author for this work

Mathematics

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

59 Scopus citations

Abstract

Let D_L denote the class of bounded, simply connected real analytic plane domains with reflection symmetries across two orthogonal axes, of which one has length L. Under generic conditions, we prove that if Ω₁, Ω₂ ∈ D_L and if the Dirichlet spectra coincide, Spec(Ω₁) = Spec(Ω₂), then Ω₁ = Ω₂ up to rigid motion.

Original language	English (US)
Pages (from-to)	628-677
Number of pages	50
Journal	Geometric and Functional Analysis
Volume	10
Issue number	3
DOIs	https://doi.org/10.1007/PL00001633
State	Published - 2000

Funding

Research partially supported by NSF grant #DMS-9703775.

ASJC Scopus subject areas

Analysis
Geometry and Topology

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10.1007/PL00001633

Cite this

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

abstract = "Let DL denote the class of bounded, simply connected real analytic plane domains with reflection symmetries across two orthogonal axes, of which one has length L. Under generic conditions, we prove that if Ω1, Ω2 ∈ DL and if the Dirichlet spectra coincide, Spec(Ω1) = Spec(Ω2), then Ω1 = Ω2 up to rigid motion.",

author = "Steve Zelditch",

note = "Funding Information: Research partially supported by NSF grant #DMS-9703775.",

year = "2000",

doi = "10.1007/PL00001633",

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journal = "Geometric and Functional Analysis",

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AU - Zelditch, Steve

N1 - Funding Information: Research partially supported by NSF grant #DMS-9703775.

PY - 2000

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N2 - Let DL denote the class of bounded, simply connected real analytic plane domains with reflection symmetries across two orthogonal axes, of which one has length L. Under generic conditions, we prove that if Ω1, Ω2 ∈ DL and if the Dirichlet spectra coincide, Spec(Ω1) = Spec(Ω2), then Ω1 = Ω2 up to rigid motion.

AB - Let DL denote the class of bounded, simply connected real analytic plane domains with reflection symmetries across two orthogonal axes, of which one has length L. Under generic conditions, we prove that if Ω1, Ω2 ∈ DL and if the Dirichlet spectra coincide, Spec(Ω1) = Spec(Ω2), then Ω1 = Ω2 up to rigid motion.

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DO - 10.1007/PL00001633

M3 - Article

AN - SCOPUS:0034396622

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JO - Geometric and Functional Analysis

JF - Geometric and Functional Analysis

IS - 3

ER -

Spectral determination of analytic bi-axisymmetric plane domains

Abstract

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