Necessary conditions for the convergence of cardinal Hermite splines as their degree tends to infinity

Author:
T. N. T. Goodman

Journal:
Trans. Amer. Math. Soc. **255** (1979), 231-241

MSC:
Primary 41A15; Secondary 41A05

DOI:
https://doi.org/10.1090/S0002-9947-1979-0542878-0

MathSciNet review:
542878

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Abstract: Let denote the class of cardinal Hermite splines of degree *n* having knots of multiplicity *S* at the integers. In this paper we show that if uniformly on **R**, where as , and *f* is bounded, then *f* is the restriction to **R** of an entire function of exponential type . In proving this result, we need to derive some extremal properties of certain splines , in particular that minimises over with .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1979-0542878-0

Keywords:
Cardinal spline interpolation,
cardinal Hermite splines,
Euler splines,
Chebyshev polynomials

Article copyright:
© Copyright 1979
American Mathematical Society