Numerische Mathematik

, Volume 15, Issue 5, pp 359–370 | Cite as

A generalization ofL-splines

  • Thomas R. Lucas


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 [6]. Theorems giving unique interpolation, integral relations, and convergence rates are established. IfL has a certain positivity property, a useful extremal result is proven.


Convergence Rate Mathematical Method Positivity Property Integral Relation Real Coefficient 
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Copyright information

© Springer-Verlag 1970

Authors and Affiliations

  • Thomas R. Lucas
    • 1
  1. 1.Department of MathematicsThe University of North Carolina at CharlotteCharlotte

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