Mathematische Annalen

, Volume 267, Issue 1, pp 37–59 | Cite as

Pólya operators I: Total positivity

  • Achim Clausing


Total Positivity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bates, P.W., Gustafson, G.B.: Green's function inequalities for two-point boundary value problems. Pac. J. Math.59, 327–343 (1975)Google Scholar
  2. 2.
    Clausing, A.: On polynomial interpolation with mixed conditions. J. Approx. Theory33, 288–295 (1981)Google Scholar
  3. 3.
    Clausing, A.: On the monotone likelihood ratio order for Lipschitz continuous densities. Statistics and Decisions2 (1984) (to appear)Google Scholar
  4. 4.
    Coppel, W.A.: Disconjugacy. In: Lecture Notes in Mathematics, Vol. 220. Berlin, Heidelberg, New York: Springer 1971Google Scholar
  5. 5.
    Davis, P.J.: Interpolation and approximation. Waltham: Blaisdell 1963Google Scholar
  6. 6.
    Gantmacher, F.R., Krein, M.G.: Oszillationsmatrizen, Oszillationskerne und kleine Schwingungen mechanischer Systeme. Berlin: Akademie-Verlag 1960Google Scholar
  7. 7.
    Karlin, S.: Total positivity. Vol. I. Stanford: Stanford University Press 1968Google Scholar
  8. 8.
    Karlin, S.: Total positivity, interpolation by splines, and Green's functions of differential operators. J. Approx. Theory4, 91–112 (1971)Google Scholar
  9. 9.
    Karon, J.M.: The sign-regularity properties of a class of Green's functions for ordinary differential equations. J. Diff. Equations6, 484–502 (1969)Google Scholar
  10. 10.
    Krein, M.G.: Sur les fonctions de Green nonsymétriques oscillatoires des opérateurs differentiels ordinaires, C. R. (Doklady) Acad. Sci. URSS (N.S.)25, 643–646 (1939)Google Scholar
  11. 11.
    Neumark, M.A.: Lineare Differentialoperatoren. Berlin: Akademie-Verlag 1963Google Scholar
  12. 12.
    Pethe, S.P., Sharma, A.: Functions analogous, to completely convex functions. Rocky Mountain J. Math.3, 591–617 (1973)Google Scholar
  13. 13.
    Pólya, G.: Bemerkung zur Interpolation und zur Näherungstheorie der Balkenbiegung. Z. angew. Math. Mech.11, 445–449 (1931)Google Scholar
  14. 14.
    Schoenberg, I.J.: On Hermite-Birkhoff interpolation. J. Math. Anal. Appl.16, 538–543 (1966)CrossRefGoogle Scholar
  15. 15.
    Schumaker, L.L.: Spline functions: basic theory. New York, Chichester, Brisbane, Toronto: Wiley 1981Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Achim Clausing
    • 1
  1. 1.Institut für Mathematische Statistik der UniversitätMünsterGermany

Personalised recommendations