Hostname: page-component-7dd5485656-bvgqh Total loading time: 0 Render date: 2025-10-31T22:13:53.815Z Has data issue: false hasContentIssue false
  • English
  • Français

On generalized subharmonic functions

Published online by Cambridge University Press:  24 October 2008

F. F. Bonsall
F. F. Bonsall
Affiliation:
King's CollegeNewcastle-on-Tyne
Get access Rights & Permissions [Opens in a new window]

Extract

In a recent paper (1) I studied a class of generalized convex functions of a single real variable which I called sub-(L) functions. Given an ordinary linear differential equation of the second order L(y) = 0, a function f(x) is sub-(L) in (a, b) if it is majorized there by the solutions of the equation. More precisely, for every x1, x2 in (a, b),f(x) ≤ F12(x) in (x1, x2), where F12 is that solution of L(y) = 0 (supposed unique) which takes the values f(xi) at xi. It was found that sub-(L) functions are characterized in a manner closely analogous to ordinary convex functions.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 46 , Issue 3 , July 1950 , pp. 387 - 395
Copyright
Copyright © Cambridge Philosophical Society 1950

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

(1)Bonsall, F. F. The characterization of generalized convex functions. Quart. J. Math. (Oxford, 2nd series) 1 (1950), 100–111.Google Scholar
(2)Littlewood, J. E.Lectures on the theory of functions (Oxford, 1944), pp. 152–62, 208, 215.Google Scholar
(3)Goursat, E.Cours d'analyse Mathematique, 3 (Paris, 1915), 225.Google Scholar
(4)Lichtenstein, L.Encyk. Math. Wiss. (Leipzig, 1923), IIC, 12, 1277–1334, particularly 1280–90.Google Scholar