Abstract

A method is given for computing the uniform norm of the cardinal Hermite spline operator. This is the operator that takes two bounded biinfinite sequences of numbers into the unique bounded spline of degree 2 k − 1( k ⩾ 2) with knots of multiplicity two at the integers and that interpolates the two given sequences for both functional and first derivative values at the integers. The computational schema relies on knowledge of the Bernoulli splines, while the theoretical aspects make use of some properties of zeros of periodic splines.

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