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A UNIQUENESS RESULT FOR THE FOURIER TRANSFORM OF MEASURES ON THE SPHERE

Published online by Cambridge University Press:  08 December 2011

FRANCISCO JAVIER GONZÁLEZ VIELI*
Affiliation:
Avenue de Montoie 45, 1007 Lausanne, Switzerland (email: francisco-javier.gonzalez@gmx.ch)
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Abstract

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A finite measure supported by the unit sphere 𝕊n−1 in ℝn and absolutely continuous with respect to the natural measure on 𝕊n−1 is entirely determined by the restriction of its Fourier transform to a sphere of radius r if and only 2πr is not a zero of any Bessel function Jd+(n−2)/2 with d a nonnegative integer.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

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