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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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Question about the regularity of fractional Heat equation
It depends on $s$, if $1/2\leq s \leq 1$, then you get analyticity. If $0<s<1/2$, then you get Gevrey class only. See Section 8.3, arXiv:1606.00873