Symmetry properties of scattering amplitudes and applications to inverse problems

DOI10.1016/0022-247X(91)90401-KzbMath0737.35152OpenAlexW2073892953MaRDI QIDQ1176896

Alexander G. Ramm

Publication date: 25 June 1992

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(91)90401-k

zbMATH Keywords

scattering amplitudesymmetric scatterer

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary value and inverse problems for harmonic functions in higher dimensions (31B20)

Related Items (3)

Necessary and sufficient condition for \(L\) to have property \(C\) ⋮ 3D inverse scattering ⋮ SOME RESULTS ON INVERSE SCATTERING

Cites Work

• Unnamed Item
• Necessary and sufficient condition for a scattering amplitude to correspond to a spherically symmetric scatterer
• Multidimensional inverse problems and completeness of the products of solutions to PDE
• Uniqueness theorems for multidimensional inverse problems with unbounded coefficients
• Numerical solution of 3D inverse scattering problems with noisy discrete fixed-energy data
• An asymptotic behavior of the S-matrix and the inverse scattering problem
• Completeness of the products of solutions of PDE and inverse problems
• Necessary and sufficient condition on the fixed-energy scattering data for the potential to be spherically symmetric
• Karp's Theorem in Acoustic Scattering Theory
• Recovery of the potential from fixed-energy scattering data

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