Regularity of the inversion problem for the Sturm-Liouville difference equation III. A criterion for regularity of the inversion problem.

We consider a difference equation where h?(0,h0],h0 is a fixed positive number, We obtain necessary and sufficient conditions under which assertions (I) and (II) hold together: (I) for a given p?[1,8), for any f?Lp(h),equation (1) has a unique solution y={yn(h)}n?Z?Lp(h) (regardless of h), and n?Z. (II) ?y?Lp(h)=c(p)??f??Lp(h) for any f?Lp(h). Here c(p) is an absolute positive constant, {Gn,m(h)}n,m?Z is the difference Green function corresponding to equation (1). [ABSTRACT FROM AUTHOR]