On Pólya frequence functions. III. The positivity of translation determinants with an application to the interpolation problem by spline curves
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- by I. J. Schoenberg and Anne Whitney PDF
- Trans. Amer. Math. Soc. 74 (1953), 246-259 Request permission
References
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F. Gantmakher and M. Krein, Oscillatory matrices and kernels and small vibrations of mechanical systems (in Russian), 2d ed., Moscow, 1950.
H. Hahn, Über das Interpolationsproblem, Math. Zeit. vol. 1 (1918) pp. 115-142.
- I. I. Hirschman Jr. and D. V. Widder, The inversion of a general class of convolution transforms, Trans. Amer. Math. Soc. 66 (1949), 135–201. MR 32817, DOI 10.1090/S0002-9947-1949-0032817-4
- M. Krein and G. Finkelstein, Sur les fonctions de Green complètement non-negatives des opérateurs différentiels ordinaires, C. R. (Doklady) Acad. Sci. URSS (N. S.) 24 (1939), 220–223 (French). MR 0002433 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.
- I. J. Schoenberg, On Pólya frequency functions. I. The totally positive functions and their Laplace transforms, J. Analyse Math. 1 (1951), 331–374 (English, with Hebrew summary). MR 47732, DOI 10.1007/BF02790092
- Isaac J. Schoenberg and Anne Whitney, Sur la positivité des déterminants de translation des fonctions de fréquence de Pólya, avec une application à un problème d’interpolation, C. R. Acad. Sci. Paris 228 (1949), 1996–1998 (French). MR 31010
Additional Information
- © Copyright 1953 American Mathematical Society
- 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