Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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
MathSciNet review: 0053177
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] F. Gantmakher and M. Krein, Oscillatory matrices and kernels and small vibrations of mechanical systems (in Russian), 2d ed., Moscow, 1950.
  • [2] H. Hahn, Über das Interpolationsproblem, Math. Zeit. vol. 1 (1918) pp. 115-142.
  • [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)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 27.0X

Retrieve articles in all journals with MSC: 27.0X

Additional Information

Article copyright: © Copyright 1953 American Mathematical Society

American Mathematical Society