Hello,

i try to understand some basic theory about linear PDE with constant coefficients.
But my knowledge about PDEs and the notation used in books is not so good.(because i have just started to study this topic).

i don't understand this statement or perhaps just the notation :

"for any a \in \mathbb{R}^n, solving P(D)u=f on  B_{R} = \{ x \in \mathbb{R}^n : \left|x\right| < R\} is equivalent to solving  P(D+a)v=g, where v=exp(-iax)*u and g=exp(-iax)f."

Ok i don't understand, why this is true. I think the author mean by P(D) some general linear PDE with constant coefficients, that is \sum_{\left| \alpha \right|\le k} b_{\alpha}*D^{\alpha}u=f with  b_{\alpha} constant coefficients.

So but what i don't know how to understand P(D+a)?
And why are both PDEs equivalent? Do you have an idea?

Regards