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

Access to Document

10.1512/iumj.2013.62.5062

Cite this

@article{5b9c6f4f852e4d84ad0f684223b1a71c,

title = "A smooth, complex generalization of the hobby-rice theorem",

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.",

keywords = "Hobby-Rice theorem",

author = "Oleg Lazarev and Lieb, \{Elliott H.\}",

year = "2013",

doi = "10.1512/iumj.2013.62.5062",

language = "English (US)",

volume = "62",

pages = "1133--1141",

journal = "Indiana University Mathematics Journal",

issn = "0022-2518",

publisher = "Department of Mathematics, Indiana University",

number = "4",

}

TY - JOUR

T1 - A smooth, complex generalization of the hobby-rice theorem

AU - Lazarev, Oleg

AU - Lieb, Elliott H.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Hobby-Rice theorem

UR - https://www.scopus.com/pages/publications/84879232951

UR - https://www.scopus.com/pages/publications/84879232951#tab=citedBy

U2 - 10.1512/iumj.2013.62.5062

DO - 10.1512/iumj.2013.62.5062

M3 - Article

AN - SCOPUS:84879232951

SN - 0022-2518

VL - 62

SP - 1133

EP - 1141

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

IS - 4

ER -

A smooth, complex generalization of the hobby-rice theorem

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this