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Results tagged with pseudo-differential-operators
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user 153260
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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Leibniz rule for square root of Laplacian
For the Leibniz rule, it is not true that
\begin{equation} (-\Delta)^{\frac12}(fg) = f (-\Delta)^{\frac12}g + g (-\Delta)^{\frac12}f \end{equation}
even in the simplest possible case, i.e. in $\mathbb …
