Almost cardinal spline interpolation (Q1813829)

Spline functions are surely interesting objects of intensive investigation. When interpolation points and knots of the relevant splines are characterized by a periodic behaviour, the interpolating problem is termed cardinal interpolation. The present paper deals with a certain generalization of known theoretical results in the subject to the ''almost cardinal'' case. Here the interpolation is cardinal except for a finite number of interpolation points and knots. The main conclusion of the work is that the wide range of almost cardinal interpolation problems (ACIP) have the same type of solutions as the corresponding cardinal interpolation problem (CIP). Preliminary results are summarized and null space explained. Existence of solution to the ACIP is also examined in detail.