A smooth complex generalization of the Hobby-Rice theorem
Oleg LazarevElliott Lieb
46Hobby-Rice theorem
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~$\pm1$ 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.
Indiana University Mathematics Journal
2013
text
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10.1512/iumj.2013.62.5062
10.1512/iumj.2013.62.5062
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Indiana Univ. Math. J. 62 (2013) 1133 - 1141
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