On the representation of band-dominant functions on the sphere using finitely many bits (Q1431334)

Let \(S^q\) be the unit sphere in \(R^{q+1}\). A band-dominant function on \(S^q\) is the restriction to \(S^q\) of an entire function of \(q+1\) complex variables having a finite exponential type in each variable. The authors develop a method to represent such a function using the values of the function at scattered poits on the sphere. It is shown that the number of the relevant bits is asymptotically the same as the metric entropy of the class of such functions with respect to any \(L^p\) norm on the sphere.