×

zbMATH — the first resource for mathematics

On Polya frequency functions. IV: The fundamental spline functions and their limits. (English) Zbl 0146.08404

PDF BibTeX XML Cite
Full Text: DOI
References:
[1] T. Bonnesen and W. Fenchel, Theorie der Konvexen Körper, Berlin, 1934. · Zbl 0008.07708
[2] H. B. Curry, Review of the paper \(\div\)9\(\div\), Math, Tables and other Aids to Comp.2 (1947), 167–169 and 211–213.
[3] H. B. Curry and I. J. Schoenberg, On Pólya frequency functions IV: The spline functions and their limits.Bull. Amer. Math. Soc., Abstract 380t,53 (1947), 1114.
[4] P. J. Davis, Interpolation and approximation, New York, 1963. · Zbl 0111.06003
[5] Ch. Hermite, Sur la formule d’interpolation de Lagrange, Oeuvres, vol. 3, 432–443. · JFM 09.0312.02
[6] I. I. Hirschman and D. V. Widder, The convolution transform, Princeton, 1955. · Zbl 0065.09301
[7] J. Korevaar and Ch. Loewner, Approximation on an arc by polynomials with restricted zeros,Indagationes Math.,26 (1964), 121–128. · Zbl 0128.29803
[8] N. E. Nörlund, Vorlesungen über Differenzenrechnung, Berlin, 1923.
[9] I. J. Schoenberg, Contributions to the problem of approximation of equidistant data by analytic functions,Quart. Appl. Math. 4 (1964) Part A, 45–99, Part B, 112–141.
[10] I. J. Schoenberg, On Pólya frequency functions I: The totally positive functions and their Laplace transforms,J. d’Analyse Math.,1 (1951), 331–374. · Zbl 0045.37602 · doi:10.1007/BF02790092
[11] I. J. Schoenberg, On Pólya frequency functions II: Variation diminishing integral operators of the convolution type,Acta Sci. Math. Szeged,12 (1950), 97–106. · Zbl 0035.35201
[12] I. J. Schoenberg and A. Whitney, On Pólya frequency functions III: The positivity of translation determinants with an application to the interpolation problem by spline curves,Trans. A.M.S.,74 (1953), 246–259. · Zbl 0051.33606
[13] I. J. Schoenberg, On the zeros of the generating functions of multiply positive sequences and functions,Annals of Math. 62 (1955), 447–471. · Zbl 0065.34301 · doi:10.2307/1970073
[14] I. J. Schoenberg, On interpolation by spline functions and its minimal properties, On Approximation Theory, International Series of Numerical Mathematics-ISNM, vol. 5 (1964), 109–129, Basel, Switzerland. · Zbl 0147.32101
[15] J. J. Schoenberg, On monosplines of least deviation and best quadrature formulae,J. SIAM Numer Analysis, Ser. B. vol.2 (1965), 144–170. · Zbl 0136.36203
[16] F. Tricomi, Über die Summe mehrerer zufälliger Veränderlichen mit konstanten Verteilungsgesetzen,Jahresber. der dentschen math. Ver.,42 (1933), 174–179. · Zbl 0006.02302
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.