Lindenstrauss' short proof of the Lyapunov Convexity Theorem: Impact and citation analysis
Department of Mathematics, University of Stellenbosch, South Africa.
This talk deals with the 1966 proof ("the slickest proof to end all proofs", [HAL, p. 156]) by J. Lindenstrauss [LIN] of the Lyapunov Convexity Theorem.
It is widely recognised that the Lindenstrauss proof revived interest in the subject of vector measures, mainly because the Convexity Theorem was now manoeuvred out of the measure theoretic protection that it had enjoyed before 1966.
The talk touches on four aspects:
(1) History and development of the Convexity Theorem up to 1966, with reference to the extreme point technique employed before 1966, and also after 1966 in the "bang-bang" principle.
(2) The role played by the 'short proof' in the breakthrough to the infinite dimensional version of the Convexity Theorem.
(3) The impact of the 'short proof' on the development and applications of the Convexity Theorem in various fields, such as Control Theory, Differential Equations, Operator Theory, Mathematical Economics, ... . Part of this discussion can be considered as a content analysis of the subject, [ROC].
(4) The citation analysis involves more than eighty books, conference proceedings and research articles either citing [LIN] or in which ideas from [LIN] play vital roles. This list, although certainly not exhaustive on this subject, includes some of the most recent publications containing applications to integration of multifunctions with respect to extreme multimeasures.
[HAL] P. R. Halmos. I want to be a mathematician. An automathography. Springer, New York, 1985.
[LIN] J. Lindenstrauss. A short proof of Liapounoff's convexity theorem. J. Math. Mech. 15 (1966), 971-972.
[ROC] M. K. Rochester. Professional communication through journal articles. Australian Academic and Research Libraries 27 (1996), 191-199. Available at URL http://ifla.inist.fr/IV/ifla61/61-rocm.htm (accessed 2000/04/11).
Date received: April 11, 2000
Copyright © 2000 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # caey-06.