Abstract
A theory of generalized splines is developed for all regular formally self adjoint differential operatorsL with real coefficients. A special case of such operators are those which may be factored in the formL =L *1 L 1, such as those related to the generalized splines of Ahlberg, Nilson, and Walsh [1, 2], and theL-splines of Schultz and Varga [6]. Theorems giving unique interpolation, integral relations, and convergence rates are established. IfL has a certain positivity property, a useful extremal result is proven.
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This research was supported in part by a NASA Traineeship, at the Georgia Institute of Technology.
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Lucas, T.R. A generalization ofL-splines. Numer. Math. 15, 359–370 (1970). https://doi.org/10.1007/BF02165507
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DOI: https://doi.org/10.1007/BF02165507