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

  • FRANCISCO JAVIER GONZÁLEZ VIELI (a1)

Abstract

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.

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References

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[1]Andrews, G. E., Askey, R. and Roy, R., Special Functions (Cambridge University Press, Cambridge, 1999).
[2]Groemer, H., Geometric Applications of Fourier Series and Spherical Harmonics (Cambridge University Press, Cambridge, 1996).
[3]Hardy, G. H., Divergent Series (Clarendon Press, Oxford, 1949).
[4]Hedenmalm, H. and Montes-Rodríguez, A., ‘Heisenberg uniqueness pairs and the Klein–Gordon equation’, Ann. of Math. (2) 173 (2011), 15071527.
[5]Lev, N., ‘Uniqueness theorems of Fourier transforms’, Bull. Sci. Math. 135 (2011), 135140.
[6]Sjölin, P., ‘Heisenberg uniqueness pairs and a theorem of Beurling and Malliavin’, Bull. Sci. Math. 135 (2011), 125133.
[7]Sogge, C. D., ‘Oscillatory integrals and spherical harmonics’, Duke Math. J. 53 (1986), 4365.
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A UNIQUENESS RESULT FOR THE FOURIER TRANSFORM OF MEASURES ON THE SPHERE

  • FRANCISCO JAVIER GONZÁLEZ VIELI (a1)

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