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This tag is for questions regarding to the Pseudo-differential operator, acting on a space of functions on a differentiable manifold, that can locally be described by definite rules using a certain function. It satisfies estimates for the derivatives analogous to the estimates for derivatives of polynomials, which are symbols of differential operators.
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Square roots of the Laplace operator
Perhaps you could see what the right-hand-side evaluates to for the eigen-functions of the Laplacian (I don't know what they are offhand but I would guess that the eigenbasis for the Laplacian on L^2( …