This is a preview of subscription content, log in via an institution to check access.
References
Amir, D., Ziegler, Z.: Expansions of generalized completely convex functions. SIAM J. Math. Anal.10, 643–654 (1979)
Berg, Ch.: Representation of completely convex functions by the extreme-point method. Enseignement. Math.23, 181–190 (1977)
Buckholtz, J.D., Shaw, J.K.: On functions expandable in Lidstone series. J. Math. Anal. Appl.47, 626–632 (1974)
Buckholtz, J.D., Shaw, J.K.: Generalized completely convex functions and Sturm-Liouville operators. SIAM J. Math. Anal.6, 812–828 (1975)
Choquet, G.: Lectures on analysis, Vols. I, II. New York: Benjamin 1969
Clausing, A.: Pólya operators. I. Total positivity. Math. Ann.267, 37–59 (1984)
Coppel, W.A.: Disconjugacy. In: Lecture Notes in Mathematics, Vol. 220. Berlin, Heidelberg, New York: Springer 1971
Dunninger, D.R.: Maximum principles for fourth order ordinary differential equations. J. Math. Anal. Appl.82, 399–405 (1981)
Karlin, S.: The existence of eigenvalues for integral operators. Trans. A.M.S.113, 1–17 (1964)
Karlin, S., Studden, W.J.: Tchebycheff systems: With applications in analysis and statistics. New York, London, Sydney: Interscience 1966
Krein, M.G., Rutman, M.A.: Linear operators leaving invariant a cone in a Banach space. Amer. Math. Soc. Trans.10, 199–325 (1962)
Lapidot, E.: On two-point expansion. J. Math. Anal. Appl.88, 508–516 (1982)
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 1972
Pethe, S.P., Sharma, A.: Modified Abel expansion and a subclass of completely convex functions. SIAM J. Math. Anal.3, 546–558 (1972)
Pethe, S.P., Sharma, A.: Functions analogous to completely convex functions. Rocky Mountain J. Math.3, 591–617 (1973)
Protter, M.H., Weinberger, H.F.: Maximum principles in differential equations. Englewood Cliffs: Prentice-Hall 1967
Schröder, J.: Operator inequalities. New York, London: Academic Press 1980
Schumaker, L.L.: Spline functions: basic theory. New York Chichester, Brisbane, Toronto: Wiley 1981
Shaw, J.K.: Series expansions and linear differential operators. SIAM J. Math. Anal.7, 311–331 (1976)
Shaw, J.K.: Analytic properties of generalized completely convex functions. SIAM J. Math. Anal.8, 271–279 (1977)
Shaw, J.K., Winfrey, W.R.: Positivity properties of linear differential operators. J. Math. Anal. Appl.65, 184–200 (1978)
Widder, D.V.: Completely convex functions and Lidstone series. Trans. A.M.S.51, 387–398 (1942)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Clausing, A. Pólya operators II: Complete concavity. Math. Ann. 267, 61–81 (1984). https://doi.org/10.1007/BF01458470
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01458470