Inverse Steklov spectral problem for curvilinear polygons › Научные исследования в СПбГУ

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Inverse Steklov spectral problem for curvilinear polygons. / Krymski, Stanislav; Levitin, Michael; Parnovski, Leonid; Polterovich, Iosif; Sher, David A.

в: International Mathematics Research Notices, Том 2021, № 1, 01.01.2021, стр. 1-37.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Krymski, S, Levitin, M, Parnovski, L, Polterovich, I & Sher, DA 2021, 'Inverse Steklov spectral problem for curvilinear polygons', International Mathematics Research Notices, Том. 2021, № 1, стр. 1-37. https://doi.org/10.1093/imrn/rnaa200

APA

Krymski, S., Levitin, M., Parnovski, L., Polterovich, I., & Sher, D. A. (2021). Inverse Steklov spectral problem for curvilinear polygons. International Mathematics Research Notices, 2021(1), 1-37. https://doi.org/10.1093/imrn/rnaa200

Vancouver

Krymski S, Levitin M, Parnovski L, Polterovich I, Sher DA. Inverse Steklov spectral problem for curvilinear polygons. International Mathematics Research Notices. 2021 Янв. 1;2021(1):1-37. https://doi.org/10.1093/imrn/rnaa200

Author

Krymski, Stanislav ; Levitin, Michael ; Parnovski, Leonid ; Polterovich, Iosif ; Sher, David A. / Inverse Steklov spectral problem for curvilinear polygons. в: International Mathematics Research Notices. 2021 ; Том 2021, № 1. стр. 1-37.

BibTeX

@article{bd219463d74c416598b71966d21168ef,

title = "Inverse Steklov spectral problem for curvilinear polygons",

abstract = " This paper studies the inverse Steklov spectral problem for curvilinear polygons. For generic curvilinear polygons with angles less than $\pi$, we prove that the asymptotics of Steklov eigenvalues obtained in arXiv:1908.06455 determines, in a constructive manner, the number of vertices and the properly ordered sequence of side lengths, as well as the angles up to a certain equivalence relation. We also present counterexamples to this statement if the generic assumptions fail. In particular, we show that there exist non-isometric triangles with asymptotically close Steklov spectra. Among other techniques, we use a version of the Hadamard--Weierstrass factorisation theorem, allowing us to reconstruct a trigonometric function from the asymptotics of its roots. ",

keywords = "math.SP, 35R30 (Primary) 35P20 (Secondary)",

author = "Stanislav Krymski and Michael Levitin and Leonid Parnovski and Iosif Polterovich and Sher, {David A.}",

year = "2021",

month = jan,

day = "1",

doi = "10.1093/imrn/rnaa200",

language = "English",

volume = "2021",

pages = "1--37",

journal = "International Mathematics Research Notices",

issn = "1073-7928",

publisher = "Oxford University Press",

number = "1",

}

RIS

TY - JOUR

T1 - Inverse Steklov spectral problem for curvilinear polygons

AU - Krymski, Stanislav

AU - Levitin, Michael

AU - Parnovski, Leonid

AU - Polterovich, Iosif

AU - Sher, David A.

PY - 2021/1/1

Y1 - 2021/1/1

N2 - This paper studies the inverse Steklov spectral problem for curvilinear polygons. For generic curvilinear polygons with angles less than $\pi$, we prove that the asymptotics of Steklov eigenvalues obtained in arXiv:1908.06455 determines, in a constructive manner, the number of vertices and the properly ordered sequence of side lengths, as well as the angles up to a certain equivalence relation. We also present counterexamples to this statement if the generic assumptions fail. In particular, we show that there exist non-isometric triangles with asymptotically close Steklov spectra. Among other techniques, we use a version of the Hadamard--Weierstrass factorisation theorem, allowing us to reconstruct a trigonometric function from the asymptotics of its roots.

AB - This paper studies the inverse Steklov spectral problem for curvilinear polygons. For generic curvilinear polygons with angles less than $\pi$, we prove that the asymptotics of Steklov eigenvalues obtained in arXiv:1908.06455 determines, in a constructive manner, the number of vertices and the properly ordered sequence of side lengths, as well as the angles up to a certain equivalence relation. We also present counterexamples to this statement if the generic assumptions fail. In particular, we show that there exist non-isometric triangles with asymptotically close Steklov spectra. Among other techniques, we use a version of the Hadamard--Weierstrass factorisation theorem, allowing us to reconstruct a trigonometric function from the asymptotics of its roots.

KW - math.SP

KW - 35R30 (Primary) 35P20 (Secondary)

UR - https://www.mendeley.com/catalogue/ef0fe55b-9781-39aa-b29b-62d50a493625/

UR - http://www.scopus.com/inward/record.url?scp=85118800992&partnerID=8YFLogxK

U2 - 10.1093/imrn/rnaa200

DO - 10.1093/imrn/rnaa200

M3 - Article

VL - 2021

SP - 1

EP - 37

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 1

ER -

ID: 84425193