One can hear the area of a torus by hearing the eigenvalues of the polyharmonic operators

• Autorzy: Guo S. , Jin J.
• Języki publikacji: EN

Abstrakty

EN

This paper considers the asymptotic properties for the spectrum of a positive integer power l of the Laplace–Beltrami operator acting on an n-dimensional torus T. If N(λ) is the number of eigenvalues counted with multiplicity, smaller than a real positive number λ, we establish a Weyl-type asymptotic formula for the spectral problem of the polyharmonic operators on T, that is, as (…), where (…) is the volume of the unit ball in Rn and Vol T is the area of T, which gives the information of the area of the torus based on the spectrum of the polyharmonic operators.

Słowa kluczowe

EN

asymptotic formula; counting function; polyharmonic operators; torus

PL

formuła asymptotyczna; funkcja liczenia; operatory poliharmoniczne; torus

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2014
• Tom: Vol. 47, nr 3
• Strony: 607--614
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Guo S.

• School of Mathematics and Statistics, Minnan Normal University Zhangzhou, 363000, People's Republic of China
• School of Mathematics and Statistics, Hubei University, Wuhan, 430062, People's Republic of China

autor

Jin J.

• School of Mathematics and Statistics, Hubei University, Wuhan, 430062, People's Republic of China

Bibliografia

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