Profiles of radially symmetric thin plate spline surfaces minimizing the
Beppo Levi energy over a compact annulus R1ββ€rβ€R2β have been
studied by Rabut via reproducing kernel methods. Motivated by our recent
construction of Beppo Levi polyspline surfaces, we focus here on minimizing the
radial energy over the full semi-axis 0<r<β. Using a L-spline
approach, we find two types of minimizing profiles: one is the limit of Rabut's
solution as R1ββ0 and R2βββ (identified as a
`non-singular' L-spline), the other has a second-derivative singularity and
matches an extra data value at 0. For both profiles and pβ[2,β], we establish the Lp-approximation order 3/2+1/p in
the radial energy space. We also include numerical examples and obtain a novel
representation of the minimizers in terms of dilates of a basis function.Comment: new figures and sub-sections; new Proposition 1 replacing old
Corollary 1; shorter proof of Theorem 4; one new referenc