Riesz bases of splines and regularized splines with multiple knots (Q1352906)

The authors prove several \(L_2\)- and Sobolev-norm stability results on the real line. First, they consider \(B\)-splines of order \(m\), defined on a bi-infinite knot sequence, where each knot is allowed to have a multiplicity of at most \(m\), and they prove a stability result for \(B\)-spline series in certain Sobolev-norms. Then they discuss generalizations of \(B\)-splines defined via their Fourier transforms using tempered distributions. A Riesz-basis property for such regularized splines is established, both in \(L_2\)- and in Sobolev-norms, under certain technical assumptions. Finally, the stability of scattered Hermite interpolation on the real line is investigated in this context.