A Smooth, Complex Generalization of the Hobby-Rice Theorem

作者:Lazarev Oleg*; Lieb Elliott H
来源:Indiana University Mathematics Journal, 2013, 62(4): 1133-1141.
DOI:10.1512/iumj.2013.62.5062

摘要

The Hobby-Rice Theorem states that, given n functions f(j), there exists a multiplier h such that the integrals of f(j) h are all simultaneously zero. This multiplier takes values +/- 1 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(j)h are all zero.

  • 出版日期2013

全文