On some problems of interpolation by \({\mathcal L}\)-splines (Q2367060)

Let \({\mathcal L}_ n ({d \over dx})\) be a linear differential operator with real constant coefficients, \(x_ \nu = \alpha_ \nu \pm i \beta_ \nu\) be the complex roots of its characteristic polynomial, and \(s\) the number of nonreal root of the characteristic polynomial. The author proves existence and uniqueness up to sign of \(2 \pi\)-periodic \({\mathcal L}_ n\)- splines with prescribed zeros \(0 \leq x_ 0 < x_ 1 < \cdots < x_{2m - 1} < 2 \pi\) under the condition \(x_{j + 1} - x_ j < {\pi \over 4s \max \beta_ \nu}\).