# Need help for construct DLSQ-spline in $B$-form

In Schumaker, Larry L. "Computing bivariate splines in scattered data fitting and the finite-element method." Numerical Algorithms 48.1-3 (2008): 237-260 (Link to journal, link to author page for PDF), Section 5, the authors claim that

It follows from standard Hilbert space approximation results that there exists a unique DLSQ-spline $s_l$ which is characterized by the property $$<s_l−f, \psi>_A=0,\quad \forall \psi\in S(\bigtriangleup)$$

I Know that every Polynomial spline $s$ can be presented in $B$-form (Bezier-Bernestein Form) that exists a $\{c_\xi\}\subseteq \mathbb{R}$ such that $$s = \sum_{|\xi|=d} c_\xi B_\xi^d.$$ In this case is standard Hilbert space approximation results like Galerkin methods (link to Galerkin wiki entry) in numerical analysis? What is "standard Hilbert space approximation results" around this content?

Any guide is welcome.