A Generalized Shannon Sampling Theorem, Fields at the Planck Scale as Band-Limited Signals

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Abstract
The Shannon Sampling Theorem is generalized for signals with arbitrarily varying bandwidth and non-equally spaced sampling. The sampling kernel is expressed explicitly in terms of the bandwidth. It is shown that such signals are equivalent to fields on certain spaces with an ultraviolet cutoff. This includes a type of short-distance structure which has been discussed for space-time at the Planck scale in the context of string theory and quantum gravity.

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