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

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  08 December 2011

FRANCISCO JAVIER GONZÁLEZ VIELI
FRANCISCO JAVIER GONZÁLEZ VIELI*
Affiliation:
Avenue de Montoie 45, 1007 Lausanne, Switzerland (email: [email protected])
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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.

Keywords

Heisenberg uniquenessFourier transformmeasuresphere

MSC classification

Secondary: 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 1 , August 2012 , pp. 78 - 82
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

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