, Volume 41, Issue 6, pp 606-612

Frames and sampling theorem

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Abstract

The sampling problem on a closed subspace Vo of L2(ℝ) is studied. For the regular sampling, a necessary and sufficient condition on the sampling theorem is presented and the sampling problem proposed by Walter is completely solved. Moreover, a representation formula for the derived function is given. The irregular sampling is studied. The results improve the ones of Walter and Liu’s.

Project supported by the National Natural Science Foundation of China (Grant No. 16971047).