A smooth, complex generalization of the hobby-rice theorem

Oleg Lazarev, Elliott H. Lieb

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

The Hobby-Rice Theorem states that, given n functions fj, there exists a multiplier h such that the integrals of fjh 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 fjh are all zero.

Original languageEnglish (US)
Pages (from-to)1133-1141
Number of pages9
JournalIndiana University Mathematics Journal
Volume62
Issue number4
DOIs
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Hobby-Rice theorem

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