Abstract
The structure of certain types of quasi shift-invariant spaces, which take the form V(ψ,X):=span‾L2{ψ(⋅−xj):j∈Z} for an infinite discrete set X=(xj)⊂R is investigated. Additionally, the relation is explored between pairs (ψ,X) and (ϕ,Y) such that interpolation of functions in V(ψ,X) via interpolants in V(ϕ,Y) solely from the samples of the original function is possible and stable. Some conditions are given for which the sampling problem is stable, and for which recovery of functions from their interpolants from a family of spaces V(ϕα,Y) is possible.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have