Abstract
Interpolation of a doubly infinite sequence of data by spline functions is studied. When the interpolation points and the knots of the interpolating splines are characterized by a periodic behavior, the interpolating problem is called Cardinal Interpolation. This work extends known results on Cardinal Interpolation to the “almost cardinal” case, where the interpolation is cardinal except for a finite number of interpolation points and knots. In passing from the cardinal to the “almost cardinal” case, the “invariance under translation” property of the interpolating spaces is lost. Thus classical arguments used in solving the cardinal case do not apply. Instead we use the intimate connection between the interpolating “almost cardinal splines” and Oscillatory Matrices. The main conclusion of this work is that a wide range of Almost Cardinal Interpolation Problems have the same type of solution as the corresponding Cardinal Interpolation Problem.
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