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A multidimensional sampling theorem and an estimate of the aliasing error. (Chinese. English summary) Zbl 1019.62500

Summary: We prove a Marcinkiewicz-type inequality for entire functions of exponential type, and from this result we obtain a Whittaker-Kotel’nikov-Shannon-type sampling theorem in the multiple variable case and determine the aliasing error on the Sobolev classes.

MSC:

62B10 Statistical aspects of information-theoretic topics
94A13 Detection theory in information and communication theory
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