Gaussian Beams and Inverse Boundary Spectral Problems

Alexander Katchalov and Matti Lassas
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Alexander Katchalov: Steklov Mathematical Institute, RAN
Matti Lassas: University of Helsinki, Department of Mathematics

A chapter in New Analytic and Geometric Methods in Inverse Problems, 2004, pp 127-163 from Springer

Abstract: Abstract In these lectures we consider inverse boundary spectral problems for elliptic operators on manifolds. This means the reconstruction of an unknown manifold and an elliptic operator on it from the knowledge of the boundary spectral data, i.e. the spectrum of the operator and normal derivatives of the normalized eigenfunctions on the boundary. Before we formulate and solve this problem in exact terms, we explain why the manifolds appear in the study of the inverse problems.

Keywords: Inverse Problem; Riemannian Manifold; Gauge Transformation; Gaussian Beam; Riccati Equation (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-08966-8_4

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DOI: 10.1007/978-3-662-08966-8_4

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