Abstract
In a recently published paper [l], the concept of complex cubic spline on a rectifiable Jordan curve was discussed together with the corresponding extension to the associated analytic spline. We introduce here complex polynomial splines which represent, simultaneously, extensions of complex cubic splines and of periodic (real) polynomial splines [2, 31. This generalization, together with the modifications in the methods of analysis which it necessitates, leads to new properties and serves to shed more light upon the structure of the spline itself. We discuss complex polynomial splines with some of their elementary properties, the associated analytic splines in various representations. We then examine in particular multiple interpolation at a point by analytic splines. In this regard, we both develop and extend some previously announced results [4].
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