Multifilters and prefilters: Uniqueness and algorithmic aspects (Q950184)

The authors characterize all valid prefilters of a given order of the simplest possible form such that the difficulties with the summation operators are intrinsic to the problem. Then, working on the symbol asssociated with the prefilter, they show that it has a simple polynomial structure such that the prefilter uses finite information only, in the sense that it maps finitely supported sequences to finitely supported sequences, at least in the cases \(p=1,2,3\). It is indicated that this is unlikely to be achieved for higher approximation orders.