Skip to main content
Log in

Pólya operators I: Total positivity

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  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. Clausing, A.: On polynomial interpolation with mixed conditions. J. Approx. Theory33, 288–295 (1981)

    Google Scholar 

  3. Clausing, A.: On the monotone likelihood ratio order for Lipschitz continuous densities. Statistics and Decisions2 (1984) (to appear)

  4. Coppel, W.A.: Disconjugacy. In: Lecture Notes in Mathematics, Vol. 220. Berlin, Heidelberg, New York: Springer 1971

    Google Scholar 

  5. Davis, P.J.: Interpolation and approximation. Waltham: Blaisdell 1963

    Google Scholar 

  6. Gantmacher, F.R., Krein, M.G.: Oszillationsmatrizen, Oszillationskerne und kleine Schwingungen mechanischer Systeme. Berlin: Akademie-Verlag 1960

    Google Scholar 

  7. Karlin, S.: Total positivity. Vol. I. Stanford: Stanford University Press 1968

    Google Scholar 

  8. Karlin, S.: Total positivity, interpolation by splines, and Green's functions of differential operators. J. Approx. Theory4, 91–112 (1971)

    Google Scholar 

  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. 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. Neumark, M.A.: Lineare Differentialoperatoren. Berlin: Akademie-Verlag 1963

    Google Scholar 

  12. Pethe, S.P., Sharma, A.: Functions analogous, to completely convex functions. Rocky Mountain J. Math.3, 591–617 (1973)

    Google Scholar 

  13. Pólya, G.: Bemerkung zur Interpolation und zur Näherungstheorie der Balkenbiegung. Z. angew. Math. Mech.11, 445–449 (1931)

    Google Scholar 

  14. Schoenberg, I.J.: On Hermite-Birkhoff interpolation. J. Math. Anal. Appl.16, 538–543 (1966)

    Article  Google Scholar 

  15. Schumaker, L.L.: Spline functions: basic theory. New York, Chichester, Brisbane, Toronto: Wiley 1981

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Clausing, A. Pólya operators I: Total positivity. Math. Ann. 267, 37–59 (1984). https://doi.org/10.1007/BF01458469

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01458469

Keywords

Navigation