INVERSE SCATTERING UP TO SMOOTH FUNCTIONS FOR THE SCHRODINGER-EQUATION IN DIMENSION .1.

For the Schrodinger equation in dimension 1 an explicit formula for th e reconstruction of the potential from the class W-n,W-1 (R) = {f(x)\d (m)/dx(m) f(x) is an element of L(1) (R), m = 0,...,n} through its ref lection coefficient up to the function from the class W-n+1,W-1 (R) is given. The necessary and sufficient conditions for the reflection coe fficient of the potential from the class L(1) (R) in order that this p otential belongs to the class W-n,W-1 (R) are given. It is shown that scattering matrix of the exponentially decreasing potential from the c lass W-n,W-1 (R) does not determine in the general case this potential up to the function from the class C-m+epsilon(R) if epsilon > 0.