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On relations between spectral and dynamical inverse data
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M. I. Belishev
Published/Copyright:
September 7, 2013
Abstract
- As is known, boundary spectral data of the compact Riemannian manifold Ω (spectrum of Laplacian with zero Dirichlet boundary condition plus traces of normal derivatives of eigenfunctions at ∂Ω) determine its boundary dynamical data (dynamical Dirichlet-to-Neumann map) R2T for all T > 0. In the paper the procedures recovering spectral data of the submanifold ΩT = {x ∈ Ω | dist(x, ∂Ω) < T} via given R2T with any prescribed T > 0 and continuing R2T from ∂Ω × (0, 2T) onto ∂Ω×(0,∞) are proposed. The procedures do not invoke solving the inverse problems; main fragment is the constructing (via R2T ) and the use of a model of dynamical system associated with ΩT.
Published Online: 2013-09-07
Published in Print: 2001-12
© 2013 by Walter de Gruyter GmbH & Co.
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Articles in the same Issue
- Contents
- On relations between spectral and dynamical inverse data
- Recovering the conductivity at the boundary from the Dirichlet to Neumann map: a pointwise result
- Regularization of degenerated equations and inequalities under explicit data parameterization
- Parabolic integrodifferential identification problems related to radial memory kernels. II
- Numerical comparison of iterative regularization methods for a parameter estimation problem in a hyperbolic PDE
- An identification problem for a one-phase Stefan problem
- Mathematical problems connected with construction of algorithms for atmosphere correction in remote sensing
