Claude Elwood Shannon's scientific contributions
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Publication (1)
Citations
... Our goal now is to specify for which subclass of functions it is possible to perfectly reconstruct the original function given only its evaluation in a countable set of points. We present a generalization of the sampling theorem (Shannon, 1949), which allows us to move from generic Hilbert spaces to a domain which is amenable to a practical implementation of FDPs, and their application to common functional representation of data such as images, data on manifolds, and more. We model these functions as objects belonging to the set of square integrable functions over C ∞ homogeneous manifolds M (such as R N , S N , etc...), i.e., the Hilbert space H = L 2 (M ). ...
