### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 1133-1141 |

Number of pages | 9 |

Journal | Indiana University Mathematics Journal |

Volume | 62 |

Issue number | 4 |

DOIs | |

State | Published - 2013 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Keywords

- Hobby-Rice theorem

## Fingerprint Dive into the research topics of 'A smooth, complex generalization of the hobby-rice theorem'. Together they form a unique fingerprint.

## Cite this

Lazarev, O., & Lieb, E. H. (2013). A smooth, complex generalization of the hobby-rice theorem.

*Indiana University Mathematics Journal*,*62*(4), 1133-1141. https://doi.org/10.1512/iumj.2013.62.5062