On deficient cubic spline interpolants (Q1185939)

This paper deals with continuously differentiable cubic splines \(s\). They are determined by the following interpolatory conditions (i) \(f(t_ i)=s(t_ i)\), \(1\leq i\leq n\) \((t_ i=x_{i-1}+mh,\;x_ i=x_ 0+ih,\;h=x_ i-x_{i-1},\;0\leq m\leq 1)\) and (ii) \(\int^{x_ i}_{x_{i- 1}}(f-s)(x)dg(x)=0\), \(1\leq i\leq n\), where \(f\) is \(\ell\)-periodic locally integrable with respect to a positive measure \(dg\). Error bounds are included.