Average sampling in spline subspaces

Let V () be a shift invariant subspace of L2 (R) generated by a Riesz or frame generator (t) in L2 (R). We assume that (t) is suitably chosen so that the regular sampling expansion f(t) = nZ f(n)Sn(t), f V () holds. In this paper, we find sufficient conditions of the generator (t) and a sequence of averaging functions {un(t)}n under which average sampling expansion f(t) = nZ < f, un > Sn(t), f V () holds. The results provided in the paper improve some previous work on average sampling in shift invariant spaces. REFERENCES

• Type: Journal
• Year: 2002
• Where: APPML
• Authors: Wenchang Sun, Xingwei Zhou
• Keywords: APPML 2002, Paper, Regular Sampling Expansion, Sufficient Conditions