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I am reading a paper, and have come across a notation I don't understand, it says: To the resulting sequence of orthonormal eigenfunctions we may associate a sequence of distributions ${dU_{k_i}}$ in $D'(S^*X)$. $(X,g)$ is a compact Riemannian manifold, but what is $S^*X$?

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I am guessing here, but most likely $S^{\star}X$ would be the space of Schwartz Bruhat functions on $X$. If you do not know what that is it is better to work with a healthier substitute and you can assume $S^{\star}X$ is space of smooth (infinitely differentiable) compactly supported real functions on $X$. –  s.b Sep 13 '12 at 17:15
    
It would help if you give the paper in question. –  Willie Wong Sep 24 '12 at 12:03

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