Multidimensional Gel'fand Inverse Boundary Spectral Problem: Uniqueness and Stability
-
Yaroslav Kurylev
Y.V.Kurylev@lboro.ac.uk
-
Matti Lassas
mjlassas@math.hut.fi
Downloads
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
Similar Articles
- K. Rajendra Prasad, Mahammad Khuddush, K. V. Vidyasagar, Infinitely many positive solutions for an iterative system of singular BVP on time scales , CUBO, A Mathematical Journal: Vol. 24 No. 1 (2022)
- Asa Ashley, Ferhan M. Atıcı, Samuel Chang, A note on constructing sine and cosine functions in discrete fractional calculus , CUBO, A Mathematical Journal: In Press
- Masaya Kawamura, On an \(a\) \(priori\) \(L^\infty\) estimate for a class of Monge-Ampère type equations on compact almost Hermitian manifolds , CUBO, A Mathematical Journal: Vol. 24 No. 2 (2022)
- Mohamed Bouaouid, Ahmed Kajouni, Khalid Hilal, Said Melliani, A class of nonlocal impulsive differential equations with conformable fractional derivative , CUBO, A Mathematical Journal: Vol. 24 No. 3 (2022)
- Buddhadev Pal, Santosh Kumar, Pankaj Kumar, Einstein warped product spaces on Lie groups , CUBO, A Mathematical Journal: Vol. 24 No. 3 (2022)
- Said Ait Temghart, Chakir Allalou, Adil Abbassi, Existence results for a class of local and nonlocal nonlinear elliptic problems , CUBO, A Mathematical Journal: Vol. 25 No. 1 (2023)
- Ganga Ram Gautam, Sandra Pinelas, Manoj Kumar, Namrata Arya, Jaimala Bishnoi, On the solution of \(\mathcal{T}-\)controllable abstract fractional differential equations with impulsive effects , CUBO, A Mathematical Journal: Vol. 25 No. 3 (2023)
- Raymond Mortini, A nice asymptotic reproducing kernel , CUBO, A Mathematical Journal: Vol. 25 No. 3 (2023)
- Abhijit Banerjee, Arpita Kundu, On uniqueness of \(L\)-functions in terms of zeros of strong uniqueness polynomial , CUBO, A Mathematical Journal: Vol. 25 No. 3 (2023)
- Dmitri V. Alekseevsky, Masoud Ganji, Gerd Schmalz, Andrea Spiro, The Levi-Civita connections of Lorentzian manifolds with prescribed optical geometries , CUBO, A Mathematical Journal: Vol. 26 No. 2 (2024)
<< < 24 25 26 27 28 29 30 31 > >>
You may also start an advanced similarity search for this article.
Downloads
Download data is not yet available.
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
Section
Articles
