I'm reading a proof of a paper and I don't understand an argument of the proof. That argument is the following:
Let $A: D(A) \subseteq L^2(\mathbb{R}) \to L^2(\mathbb{R}) $ be a constant coefficients differential operator of order $2n$. The restriction of $A$ to $L^2(I)$ ($I$ is an interval in $\mathbb{R}$) in the sense of quadratic forms is precisely the restriction which satisfies the Dirichlet boundary conditions (that boundary conditions are $u(c)=u'(c)= \cdots = u^{(n-1)}(c)=0$ at any finite boundary point $c$).
Can you help me to show the last statement, please?. I don't know what "restriction in the sense of quadratic forms" means. Can you give me a reference on that subject, please?.
Thanks in advance for any help.