I am confused about how to obtain the least squares estimator of this problem: $$ \inf\{||s-\lambda||_2:s\in S_{k,v}\}=||P_k\lambda-\lambda||_2\tag{1} $$ where $||\lambda||_2=\{\int_0^1\lambda^2(x)dx\}^{1/2}$, and $S_{k,v}$ is called the class of all B-splines of degree $v$ with $k$-equspaced knots. This paper(pages 277) states that \begin{equation}\tag{2} (P_km)(x)=\bar{b}_k'\bar{A}_k^{-1}B_k(x) \end{equation} where $\bar{b}_k'=\int_0^1m(x)B_k(x)dx,\bar{A}_k=\int_0^1B_k(x)B_k'(x)dx$, and $B_k(x)$ is B-splines of degree $v$.
I am not sure how to obtain equation(2) from (1), which looks like a least squares estimator,but in intergral format.