Notes on Spline Functions, III: On the Convergence of the Interpolating Cardinal Splines as Their Degree Tends to Infinity.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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In previous papers special classes of functions fx, defined for all real x, were established with the property that if S sub mx is the unique cardinal spline interpolant of fx, of degree 2m-1, then S sub mx converges to fx, uniformally for all real x. Reporting about these results in a monograph, the author raised the question of the existence of a comprehensive theory that would contain these separate results as special cases. Such a theory is developed in the present note. It is based on the properties of the so-called exponential Euler spline and the proof of the more general result is far simpler than the proofs given earlier for the special cases. Modified author abstract
- Theoretical Mathematics