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Necessary Conditions for the Convergence of Cardinal Hermite Splines as their Degree Tends to Infinity
Let ${\mathcal {S}_{n,s}}$ denote the class of cardinal Hermite splines of degree n having knots of multiplicity S at the integers. In this paper we show that if ${f_n} \to f$ uniformly on R, where ${f_n} \in {\mathcal {S}_{{i_{n,s}}}} {i_n} \to \infty$ as $n \to \infty$, and f is bounded, …