ABSTRACT
Definition 2.1.1. The space consists of all infinitely differentiable complexvalued functions φ(x) defined in the n-dimensional space and decaying at infinity, together with all their derivatives, faster than any negative power of
. For , we use the notation
(2.1.1)
where p=(p1,…, pn) is a multi-index with integer components, ,
The topology in S is defined by the norms (2.1.1). Accordingly, a sequence converges to as k→∞, if |[(φ−φk]|m→0 for every m=1, 2,….
