Sampling set conditions in weighted multiply generated shift-invariant spaces and their applications

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Abstract

In this paper, we investigate the non-uniform weighted average sampling for the weighted multiply generated shift-invariant space. The conditions for sampling point set to be a set of sampling for the weighted multiply generated shift-invariant space are obtained. Furthermore, the explicit bound expressions of a set of sampling inequalities for this shift-invariant spaces also are obtained.

Keywords

Non-uniform sampling
Sampling set
Weighted multiply generated shift-invariant space
Spline subspace

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