On the inverse spectral problem for Euclidean triangles-Reference-Cited by-同舟云学术

On the inverse spectral problem for Euclidean triangles

Published:2010-12-08 Issue:2130 Volume:467 Page:1546-1562
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Antunes Pedro R. S.¹,Freitas Pedro¹²

Affiliation:

1. Group of Mathematical Physics of the University of Lisbon, Complexo Interdisciplinar, Avenida do Professor Gama Pinto 2, 1649-003 Lisboa, Portugal

2. Department of Mathematics, Faculdade de Motricidade Humana (TU Lisbon), Cruz Quebrada, P-1495-688 Cruz Quebrada-Dafundo, Portugal

Abstract

We consider the inverse spectral problem for the Laplace operator on triangles with Dirichlet boundary conditions, providing numerical evidence to the effect that the eigenvalue triplet ( λ 1 , λ 2 , λ 3 ) is sufficient to determine a triangle uniquely. On the other hand, we show that other combinations such as ( λ 1 , λ 2 , λ 4 ) will not be enough, and that there will exist at least two triangles with the same values on these triplets.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2010.0540

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