the name of this operator is one-parameter semigroup

for example  $ EXP[\frac{ \theta }{2}\frac{\partial^2}{\partial \overrightarrow{v}^2}]f$，

$ f$is the function of $\overrightarrow{v}$

what is the meaning of this operator

is $ EXP[\frac{ \theta }{2}\frac{\partial^2}{\partial \overrightarrow{v}^2}]f$ means $EXP[\frac{ \theta }{2}\frac{\partial^2 f}{\partial \overrightarrow{v}^2}]$ ?

The name of the operator $ EXP[\frac{ \theta }{2}\frac{\partial^2}{\partial \overrightarrow{v}^2}]$ is one-parameter semigroup.

For example one writes $ EXP[\frac{ \theta }{2}\frac{\partial^2}{\partial \overrightarrow{v}^2}]f$, where $f$ is a function of $\overrightarrow{v}$.

What is the meaning of this operator?

Does $ EXP[\frac{ \theta }{2}\frac{\partial^2}{\partial \overrightarrow{v}^2}]f$ mean $EXP[\frac{ \theta }{2}\frac{\partial^2 f}{\partial \overrightarrow{v}^2}]$ ?

the name of this operator is one-parameter semigroup

for example $ EXP[\frac{ \theta }{2}\frac{\partial^2}{\partial \overrightarrow{v}^2}]f$，

$ f$is the function of $\overrightarrow{v}$

what is the meaning of this operator

the name of this operator is one-parameter semigroup

for example $ EXP[\frac{ \theta }{2}\frac{\partial^2}{\partial \overrightarrow{v}^2}]f$，

$ f$is the function of $\overrightarrow{v}$

what is the meaning of this operator

is $ EXP[\frac{ \theta }{2}\frac{\partial^2}{\partial \overrightarrow{v}^2}]f$ means $EXP[\frac{ \theta }{2}\frac{\partial^2 f}{\partial \overrightarrow{v}^2}]$ ?