From the representation of the Cauchy problem u't= Delta u-v(r)u u mod t=+0= delta (r-r') (r=(x,y,z), r'=(x',y',z')), as a Wiener continual integral, the author derives nonlinear integral equations of the second kind for well known inverse problems of the spectral theory of the Schrodinger operator H=- Delta + nu (r) in the cases where nu (r)=v( mod r mod ) or nu (r)= Sigma j=1N nu j( mod rj0-r mod ) (rj0=(xj0,yj0,zj0) are fixed points). Theorems and formulae relating the spectral kernel theta (r,r', lambda , in ) of the family of the operators H=- Delta + in nu (r) ( in being an arbitrary real parameter) to the potential nu (r) are found.