Alexander G.Ramm – Inverse Problems

Alexander G.Ramm – Inverse Problems

Here’s what you’ll get:

• recovery of a potential from I-function and applications to classical and new inverse scattering and spectral problems,
• study of inverse problems with”incomplete data”,
• study of some new inverse problems for parabolic and hyperbolic equations,
• discussion of some non-overdetermined inverse problems,
• a study of inverse problems arising in the theory of ground-penetrating radars,
• development of DSM (dynamical systems method) for solving ill-posed nonlinear operator equations,
• comparison of the Ramm’s inversion method for solving fixed-energy inverse scattering problem with the method based on the Dirichlet-to-Neumann map,
• derivation of the range of applicability and error estimates for Born’s inversion,
• a study of some integral geometry problems, including tomography,
• inversion formulas for the spherical means,
• proof of the invertibility of the steps in the Gel’fand-Levitan and Marchenko inversion procedures,
• derivation of the inversion formulas and stability estimates for the multidimensional inverse scattering problems with fixed-energy noisy discrete data,
• new uniqueness and stability results in obstacle inverse scattering,
• formulation and a solution of an inverse problem of radiomeasurements,
• methods for finding small inhomogeneities from surface scattering data.

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