What does it mean, that the interpolants are choosen from BL-space of distributions? I would like to understand this paper: Reconstruction and Representation of 3D Objects with Radial Basis Functions It is clear, until the beginning of the 4th page. It states, that: The interpolant will be chosen from BL ($ \mathbb{R}^3 $), the Beppo-Levi space of distributions on $ \mathbb{R}^3 $ with square integrable second derivatives. This space is sufficiently large to have many solutions to the problem. I've found the definition of Beppo-Levi space, but I am not able to understand it in this form. I have no idea what Beppo-Levi space, or an interpolant from Beppo-Levi space of distributions means.

It's the so-called native space of the RBFs the authors will be working with, see Wendland's "Scattered Data Approximation". Basically, when looking for an interpolating function you assume its smoothness class, e.g. functions with square integrable second derivatives. This allows to define different norms and choose for each the smoothest interpolant -- different RBFs.