New Types of Relations in Finite Field Theory.

also satisfies condition (v), and let { I} and { 4,, } be each a set of m linearly independent eigen solutions of H* corresponding to the eigen values i and-i, respectively. If we can find a mapping of 6 on to 22(A) of the form (3) which maps the sets of elements (PM, } and { J,J, } on to sets of functions { (p,,(x) I and { +,(x) } satisfying condition (e), then this mapping takes H into a self-adjoint differential operator of Mlh order defined in V2(A). In the same way the generalized class P of mth order in ?2(A) can be extended to a generalized class P of m' order in S. We omit the details.