Standard

An inequality for the Steklov spectral zeta function of a planar domain. / Jollivet, Alexandre; Sharafutdinov, Vladimir.

In: Journal of Spectral Theory, Vol. 8, No. 1, 01.01.2018, p. 271-296.

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

Harvard

Jollivet, A & Sharafutdinov, V 2018, 'An inequality for the Steklov spectral zeta function of a planar domain', Journal of Spectral Theory, vol. 8, no. 1, pp. 271-296. https://doi.org/10.4171/JST/196

APA

Jollivet, A., & Sharafutdinov, V. (2018). An inequality for the Steklov spectral zeta function of a planar domain. Journal of Spectral Theory, 8(1), 271-296. https://doi.org/10.4171/JST/196

Vancouver

Jollivet A, Sharafutdinov V. An inequality for the Steklov spectral zeta function of a planar domain. Journal of Spectral Theory. 2018 Jan 1;8(1):271-296. doi: 10.4171/JST/196

Author

Jollivet, Alexandre ; Sharafutdinov, Vladimir. / An inequality for the Steklov spectral zeta function of a planar domain. In: Journal of Spectral Theory. 2018 ; Vol. 8, No. 1. pp. 271-296.

BibTeX

@article{96b903c55df242288b5b7fa9df2c90e7,
title = "An inequality for the Steklov spectral zeta function of a planar domain",
abstract = "We consider the zeta function Ω for the Dirichlet-to-Neumann operator of a simply connected planar domain Ωbounded by a smooth closed curve. We prove that, for a fixed real s satisfying jsj > 1 and fixed length L.@ Ω/ of the boundary curve, the zeta function Ω.s/ reaches its unique minimum when Ωis a disk. This result is obtained by studying the difference Ω(s)-2L.@ Ω/ 2 π R.s/,where R stands for the classicalRiemann zeta function. The difference turns out to be non-negative for real s satisfying jsj > 1. We prove some growth properties of the difference as s →±∞ Two analogs of these results are also provided.",
keywords = "Dirichlet-to-Neumann operator, Inverse spectral problem, Steklov spectrum, Zeta function, inverse spectral problem, EIGENVALUES, NEUMANN OPERATOR, zeta function",
author = "Alexandre Jollivet and Vladimir Sharafutdinov",
year = "2018",
month = jan,
day = "1",
doi = "10.4171/JST/196",
language = "English",
volume = "8",
pages = "271--296",
journal = "Journal of Spectral Theory",
issn = "1664-039X",
publisher = "European Mathematical Society Publishing House",
number = "1",

}

RIS

TY - JOUR

T1 - An inequality for the Steklov spectral zeta function of a planar domain

AU - Jollivet, Alexandre

AU - Sharafutdinov, Vladimir

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We consider the zeta function Ω for the Dirichlet-to-Neumann operator of a simply connected planar domain Ωbounded by a smooth closed curve. We prove that, for a fixed real s satisfying jsj > 1 and fixed length L.@ Ω/ of the boundary curve, the zeta function Ω.s/ reaches its unique minimum when Ωis a disk. This result is obtained by studying the difference Ω(s)-2L.@ Ω/ 2 π R.s/,where R stands for the classicalRiemann zeta function. The difference turns out to be non-negative for real s satisfying jsj > 1. We prove some growth properties of the difference as s →±∞ Two analogs of these results are also provided.

AB - We consider the zeta function Ω for the Dirichlet-to-Neumann operator of a simply connected planar domain Ωbounded by a smooth closed curve. We prove that, for a fixed real s satisfying jsj > 1 and fixed length L.@ Ω/ of the boundary curve, the zeta function Ω.s/ reaches its unique minimum when Ωis a disk. This result is obtained by studying the difference Ω(s)-2L.@ Ω/ 2 π R.s/,where R stands for the classicalRiemann zeta function. The difference turns out to be non-negative for real s satisfying jsj > 1. We prove some growth properties of the difference as s →±∞ Two analogs of these results are also provided.

KW - Dirichlet-to-Neumann operator

KW - Inverse spectral problem

KW - Steklov spectrum

KW - Zeta function

KW - inverse spectral problem

KW - EIGENVALUES

KW - NEUMANN OPERATOR

KW - zeta function

UR - http://www.scopus.com/inward/record.url?scp=85042864545&partnerID=8YFLogxK

U2 - 10.4171/JST/196

DO - 10.4171/JST/196

M3 - Article

AN - SCOPUS:85042864545

VL - 8

SP - 271

EP - 296

JO - Journal of Spectral Theory

JF - Journal of Spectral Theory

SN - 1664-039X

IS - 1

ER -

ID: 10422279