IUMJ

Title: A smooth complex generalization of the Hobby-Rice theorem

Authors: Oleg Lazarev and Elliott Lieb

Issue: Volume 62 (2013), Issue 4, 1133-1141

Abstract:

The Hobby-Rice Theorem states that, given $n$ functions $f_j$, there exists a multiplier $h$ such that the integrals of $f_jh$ are all simultaneously zero. This multiplier takes values~$\pm1$ and is discontinuous. We show how to find a multiplier that is infinitely differentiable, takes values on the unit circle, and is such that the integrals of $f_jh$ are all zero.