ABSTRACT
Definition 8.1.1. Let ε be a set of indices k=(k1,…, kn) and let A be a pseudodifference operator (see Definition 7.1.7). The operator pA defined by
is called the restriction of A to the set ε. Definition 8.1.2. The problem of restriction of a pseudodifference operator is formulated as follows: given a grid function f(k1,…, kn)=f(k) for , find a grid function x(k) defined on the same set of nodes and satisfying the relations
(8.1.1)
Let us examine some restriction problems. Here, we assume that the symbol of the pseudodifference operator A does not depend on k, and the symbol is denoted by . Definition 8.1.3. Consider the sets of integer numbers
Problems of restriction to ε1 or ε2 are called problems of restriction to L+ or L−, respectively. For k=(k1,…, kn) and , problems of restriction to ε1i or ε2i are called problems of restriction to Li+ or Li−, respectively.
