A smooth, complex generalization of the hobby-rice theorem

Oleg Lazarev; Elliott H. Lieb

doi:10.1512/iumj.2013.62.5062

A smooth, complex generalization of the hobby-rice theorem

Oleg Lazarev, Elliott H. Lieb

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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 ±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_jh are all zero.

Original language	English (US)
Pages (from-to)	1133-1141
Number of pages	9
Journal	Indiana University Mathematics Journal
Volume	62
Issue number	4
DOIs	https://doi.org/10.1512/iumj.2013.62.5062
State	Published - 2013

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Hobby-Rice theorem

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10.1512/iumj.2013.62.5062

Cite this

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A smooth, complex generalization of the hobby-rice theorem

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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