On Functions with Zero Integral Moments over Balls of Fixed Radius |
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Authors: | V. V. Volchkov Vit. V. Volchkov |
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Affiliation: | 1.Donetsk National University,Donetsk,Ukraine |
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Abstract: | We consider precise conditions ensuring that a function having zero integrals over all balls of fixed radius is equal to zero. The case where, together with zero integrals for f over congruent balls, the functions xjf for all j have zero integrals over these balls is completely investigated. An inversion formula recovering a function in the class C∞ from indicated integral moments is derived. |
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