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On Pólya frequence functions. III. The positivity of translation determinants with an application to the interpolation problem by spline curves


Authors: I. J. Schoenberg and Anne Whitney
Journal: Trans. Amer. Math. Soc. 74 (1953), 246-259
MSC: Primary 27.0X
DOI: https://doi.org/10.1090/S0002-9947-1953-0053177-X
MathSciNet review: 0053177
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  • [3] I. I. Hirschman and D. V. Widder, The inversion of a general class of convolution transforms, Trans. Amer. Math. Soc. vol. 66 (1949) pp. 135-201. MR 0032817 (11:350g)
  • [4] M. Krein and G. Finkelstein, Sur les fonctions de Green complètement non-négatives des opérateurs differentiels ordinaires, C. R. (Doklady) Acad. Sci. URSS. vol. 24 (1939) pp. 220-223. MR 0002433 (2:52c)
  • [5] I. J. Schoenberg, Contributions to the problem of approximation of equidistant data by analytic functions, Parts A and B, Quarterly of Applied Mathematics vol. 4 (1946) pp. 45-99, 112-141.
  • [6] -, On Pólya frequency functions I. The totally positive functions and their Laplace transforms, Journal d'Analyse Mathématique vol. 1 (1951) pp. 331-374. MR 0047732 (13:923c)
  • [7] I. J. Schoenberg and Anne Whitney, Sur la positivité des déterminants de translations des fonctions de fréquence de Pólya avec une application au problème d'interpolation par les fonctions "spline," C. R. Acad. Sci. Paris vol. 228 (1949) pp. 1996-1998. MR 0031010 (11:86e)

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DOI: https://doi.org/10.1090/S0002-9947-1953-0053177-X
Article copyright: © Copyright 1953 American Mathematical Society

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