TY - JOUR
T1 - The Factorization Method to Solve a Class of Inverse Potential Scattering Problems for Schrödinger Equations
AU - Li , Yuan
AU - Ma , Fuming
JO - Communications in Mathematical Research 
VL - 4
SP - 321
EP - 336
PY - 2021
DA - 2021/05
SN - 26
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19130.html
KW - factorization method, inverse scattering, Schrödinger equation, interior transmission
problem.
AB - <p style="text-align: justify;">This paper is concerned with the inverse scattering problems for Schrödinger equations
with compactly supported potentials. For purpose of reconstructing the support of the potential,
we derive a factorization of the scattering amplitude operator $A$ and prove that the ranges of $(A^∗A) ^{1/4}$ and $G$ which maps more general incident fields than plane waves into the scattering
amplitude coincide. As an application we characterize the support of the potential using only the
spectral data of the operator $A$.</p>