Existence of Good and Best Approximations on Unbounded Domains by Exponential Sums in Several Independent Variables.

摘要

This paper considers the problem of using exponential sums to approximate a given complex-valued function f defined on the possibly unbounded domain D in R to the mth power. The existence of a best approximation is established from the set of exponential sums having order at most n and formulate a Weierstrass-type density theorem. Doing so extends previously known results which apply only in the special cases where D is bounded or where m = 1.