Abstract
A band-dominant function on the Euclidean sphere embedded in R q+1 is the restriction to this sphere of an entire function of q+1 complex variables having a finite exponential type in each of its variables. We develop a method to represent such a function using finitely many bits, using the values of the function at scattered sites on the sphere. The number of bits required in our representation is asymptotically the same as the metric entropy of the class of such functions with respect to any of the L p norms on the sphere.
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Mhaskar, H., Narcowich, F. & Ward, J. On the Representation of Band-Dominant Functions on the Sphere Using Finitely Many Bits. Advances in Computational Mathematics 21, 127–146 (2004). https://doi.org/10.1023/B:ACOM.0000016434.97920.1f
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DOI: https://doi.org/10.1023/B:ACOM.0000016434.97920.1f