Advertisement

Mathematische Annalen

, Volume 267, Issue 1, pp 61–81 | Cite as

Pólya operators II: Complete concavity

  • Achim Clausing
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Amir, D., Ziegler, Z.: Expansions of generalized completely convex functions. SIAM J. Math. Anal.10, 643–654 (1979)Google Scholar
  2. 2.
    Berg, Ch.: Representation of completely convex functions by the extreme-point method. Enseignement. Math.23, 181–190 (1977)Google Scholar
  3. 3.
    Buckholtz, J.D., Shaw, J.K.: On functions expandable in Lidstone series. J. Math. Anal. Appl.47, 626–632 (1974)Google Scholar
  4. 4.
    Buckholtz, J.D., Shaw, J.K.: Generalized completely convex functions and Sturm-Liouville operators. SIAM J. Math. Anal.6, 812–828 (1975)Google Scholar
  5. 5.
    Choquet, G.: Lectures on analysis, Vols. I, II. New York: Benjamin 1969Google Scholar
  6. 6.
    Clausing, A.: Pólya operators. I. Total positivity. Math. Ann.267, 37–59 (1984)Google Scholar
  7. 7.
    Coppel, W.A.: Disconjugacy. In: Lecture Notes in Mathematics, Vol. 220. Berlin, Heidelberg, New York: Springer 1971Google Scholar
  8. 8.
    Dunninger, D.R.: Maximum principles for fourth order ordinary differential equations. J. Math. Anal. Appl.82, 399–405 (1981)Google Scholar
  9. 9.
    Karlin, S.: The existence of eigenvalues for integral operators. Trans. A.M.S.113, 1–17 (1964)Google Scholar
  10. 10.
    Karlin, S., Studden, W.J.: Tchebycheff systems: With applications in analysis and statistics. New York, London, Sydney: Interscience 1966Google Scholar
  11. 11.
    Krein, M.G., Rutman, M.A.: Linear operators leaving invariant a cone in a Banach space. Amer. Math. Soc. Trans.10, 199–325 (1962)Google Scholar
  12. 12.
    Lapidot, E.: On two-point expansion. J. Math. Anal. Appl.88, 508–516 (1982)Google Scholar
  13. 13.
    Leeming, D., Sharma, A.: A generalization of the class of completely convex functions. In: Incqualities-III (ed. O. Shisha) pp. 177–199. New York, London: Academic Press 1972Google Scholar
  14. 14.
    Pethe, S.P., Sharma, A.: Modified Abel expansion and a subclass of completely convex functions. SIAM J. Math. Anal.3, 546–558 (1972)Google Scholar
  15. 15.
    Pethe, S.P., Sharma, A.: Functions analogous to completely convex functions. Rocky Mountain J. Math.3, 591–617 (1973)Google Scholar
  16. 16.
    Protter, M.H., Weinberger, H.F.: Maximum principles in differential equations. Englewood Cliffs: Prentice-Hall 1967Google Scholar
  17. 17.
    Schröder, J.: Operator inequalities. New York, London: Academic Press 1980Google Scholar
  18. 18.
    Schumaker, L.L.: Spline functions: basic theory. New York Chichester, Brisbane, Toronto: Wiley 1981Google Scholar
  19. 19.
    Shaw, J.K.: Series expansions and linear differential operators. SIAM J. Math. Anal.7, 311–331 (1976)Google Scholar
  20. 20.
    Shaw, J.K.: Analytic properties of generalized completely convex functions. SIAM J. Math. Anal.8, 271–279 (1977)Google Scholar
  21. 21.
    Shaw, J.K., Winfrey, W.R.: Positivity properties of linear differential operators. J. Math. Anal. Appl.65, 184–200 (1978)Google Scholar
  22. 22.
    Widder, D.V.: Completely convex functions and Lidstone series. Trans. A.M.S.51, 387–398 (1942)Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

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

Personalised recommendations