Multidimensional Gel'fand Inverse Boundary Spectral Problem: Uniqueness and Stability

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Abstract

The paper is devoted to the reconstruction of a compact Riemannian manifold from the Gel'fand boundary spectral data. These data consist of the eigenvalues and the boundary values of the eigenfunctions of the Laplace operator with the Neumann boundary condition. We provide the reconstruction procedure using the geometric variant of the boundary control method. In addition to the uniqueness and reconstruction results, we sketch recent developments in the conditional stability in this problem. These conditions are formulated in terms of some geometric restrictions traditional for the theory of geometric convergence.

Keywords

boundary spectral problem , conditional stability , Laplace operator , Riemannian manifold
  • Yaroslav Kurylev Loughborough University, Department of Mathematical Sciences, Leicestershire LE11 3TU, UK.
  • Matti Lassas Helsinki University of Technology, lnstitute of Mathematics. PO Box 1100, 02015 TKK, Finland.
  • Pages: 41–59
  • Date Published: 2006-04-01
  • Vol. 8 No. 1 (2006): CUBO, A Mathematical Journal

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Published

2006-04-01

How to Cite

[1]
Y. Kurylev and M. Lassas, “Multidimensional Gel’fand Inverse Boundary Spectral Problem: Uniqueness and Stability”, CUBO, vol. 8, no. 1, pp. 41–59, Apr. 2006.

Issue

Vol. 8 No. 1 (2006): CUBO, A Mathematical Journal

Section

Articles