I Fourier transform on manifolds

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Is there a generalized form of the Fourier transform applicable to all manifolds, such that the Fourier transform in Euclidean space is a special case?
 

Orodruin

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The corresponding thing in a (Riemannian or pseudo-Riemannian) manifold would be to look for expansions in terms of eigenfunctions of the operator ##\nabla^2 = \nabla_a \nabla^a = g^{ab} \nabla_a \nabla_b##.
 

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