4 papers · 1 filter
Integral Operators Basic in Random Fields Estimation Theory
Alexander Kozhevnikov, Alexander G. Ramm
The paper deals with the basic integral equation of random field estimation theory by the criterion of minimum of variance of the error estimate. This integral equation is of the f…
Compactness of the embedding operators for rough domains
Vladimir Gol'dshtein, Alexander G. Ramm
New classes of non-smooth bounded domains D, for which the embedding operator from H^1(D) into L^2(D) is compact are introduced. Examples are given and applications to scattering b…
Stability of solutions to inverse scattering problems with fixed-energy data
Alexander G. Ramm
A review of the author's results is given. Inversion formulas and stability estimates for the solutions to 3D inverse scattering problems with fixed-energy data are obtained. Inver…
Linear ill-posed problems and dynamical systems
Alexander G. Ramm
A linear equation Au=f (1) with a bounded, injective, but not boundedly invertible linear operator in a Hilbert space H is studied. A new approach to solving linear ill-posed probl…