Multidimensional inverse scattering: An orthogonalization formulation
نویسندگان
چکیده
منابع مشابه
Multidimensional Inverse Scattering with Fixed-Energy Data
1 Introduction In this lecture the author reviews his results on multidimensional inverse scattering. References to the works of other authors can be found in [20]. Five topics are briefly discussed:-1) property C with constraints and new type of the uniqueness theorems for inverse scattering,-2) inversion of noisy discrete fixed-energy 3D scattering data and error estimates,-3) variational pri...
متن کاملNovel Formulation of Inverse Scattering and Characterization of Scattering Data
In this article we formulate the direct and inverse scattering theory for the focusing matrix Zakharov-Shabat system as the construction of a 1, 1-correspondence between focusing potentials with entries in L1(R) and Marchenko integral kernels, given the fact that these kernels encode the usual scattering data (one reflection coefficient, the discrete eigenvalues with positive imaginary part, an...
متن کاملA New Look at the Multidimensional Inverse Scattering Problem
As a prototype of an evolution equation we consider the Schrödinger equation i(d/dt)Ψ(t) = H Ψ(t), H = H0 + V (x) for the Hilbert space valued function Ψ(·) : R → H = L2(Rν) which describes the state of the system at time t in space dimension ν ≥ 2. The kinetic energy operator H0 may be H0 = −(1/2m)∆ (nonrelativistic quantum mechanics for a particle of mass m), H0 = √ −∆+m2 (relativistic kinema...
متن کاملMultidimensional Inverse Quantum Scattering Problem and Wiener-Hopf Factorization*
\Ve consider the direct and inverse scattering for the n-dimensional Schrodinger equation, n 2: 2, with a potential having no spherical symmetry. Sufficient conditions are given for the existence of a Wiener-Hopf factorization of the corresponding scattering operator. This factorization leads to the solution of a related Riemann-Hilbert problem, which plays a key role in inverse scattering.
متن کاملMR-EPT Reconstruction Using an Inverse Formulation
The electrical conductivity of soft tissues can be reconstructed from imaging with MR Electrical Properties Tomography (MR-EPT). The reconstruction method used here is based on an inverse problem formulation, with two advantages over a direct inversion approach: a) no spatial differentiation is needed and b) the regularization term determines the resolution of the reconstructed data. The proces...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 1987
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.527503