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 * L1, such as those related to the generalized splines of Ahlberg, Nilson, and Walsh [1, 2], and theL-splines of Schultz and Varga . Theorems giving unique interpolation, integral relations, and convergence rates are established. IfL has a certain positivity property, a useful extremal result is proven.
KeywordsConvergence Rate Mathematical Method Positivity Property Integral Relation Real Coefficient
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