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Here is a good reference for this
In Chapter 12 it explains how to construct $f(A)$ when $A$ is elliptic selfadjoint of order $1$, $A\geq 0$, and $f$ is a smooth symbol of order $m$, i.e., $f$ is smooth and $$ f^{(k)}(\lambda)= O(|\lambda|^{m-k}),\;\;\lambda\to\infty $$, for any nonnegative integer $k$ |
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Here is a good reference for this
In Chapter 12 it explains how to construct $f(A)$ when $A$ is selfadjoint of order $1$, $A\geq 0$, and $f$ is a smooth symbol of order $m$.m$, i.e., $f$ is smooth and $$ f^{(k)}(\lambda)= O(|\lambda|^{m-k}),\;\;\lambda\to\infty $$, for any nonnegative integer $k$ |
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Here is a good reference for this
In Chapter 12 it explains how to construct $f(A)$ when $A$ is selfadjoint of order $1$, $A\geq 0$, and $f$ is a symbol of order $m$. |
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