Stability and Reconstruction in Gel'fand Inverse Boundary Spectral Problem

2002/01/30 by Atsushi Katsuda, Katsuda, Atsushi, Yaroslav Kurylev +3 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.math/0201309

arxiv created 2002/01/30 · arxiv updated 2009/11/30

Abstract

We consider stability and approximate reconstruction of Riemannian manifold when the finite number of eigenvalues of the Laplace-Beltrami operator and the boundary values of the corresponding eigenfunctions are given. The reconstruction can be done in stable way when manifold is a priori known to satisfy natural geometrical conditions related to curvature and other invariant quantities.

Cited by

• Stability of Gel'fand's inverse interior spectral problem for Schrödinger operators

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