Sankhya: The Indian Journal of Statistics
2000, Volume 62, Series A, Pt. 3, pp. 419--424
SOME QUESTIONS ON INTEGRAL GEOMETRY ON RIEMANNIAN MANIFOLDS
VISHWAMBHAR PATI and ALLADI SITARAM, Indian Statistical Institute, Bangalore
SUMMARY. It is a surprising but known fact that an L1 function on Rn is determined once all its spherical averages with centres coming from certain ``small'' sets are known. We generalise this result to complete connected real-analytic Riemannian manifolds with a real-analytic metric (with some curvature restrictions), where superisothermal sets play the same role as balls do in the case of Euclidean space.
AMS (1991) subject classification. 53C65.
Key words and phrases. Integral geometry, heat kernel, Riemannian manifold.
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