Resolvent identity
= Resolvent identity
For two points $z,w$ in the resolvent set of an operator $A$,
$$
R(z,A)-R(w,A)=(w-z)R(z,A)R(w,A).
$$
In particular, the <resolvent operator> is differentiable and $\partial_zR(z,A)=-R(z,A)^2$.
= Resolvent identity
For two points $z,w$ in the resolvent set of an operator $A$,
$$
R(z,A)-R(w,A)=(w-z)R(z,A)R(w,A).
$$
In particular, the <resolvent operator> is differentiable and $\partial_zR(z,A)=-R(z,A)^2$.