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Generic Differentiability of Convex Functions and Monotone Operators


Verona, Maria Elena (1989) Generic Differentiability of Convex Functions and Monotone Operators. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/be7m-vv03.


The aim of this paper is to investigate to what extent the known theory of subdifferentiability and generic differentiability of convex functions defined on open sets can be carried out in the context of convex functions defined on not necessarily open sets. Among the main results obtained I would like to mention a Kenderov type theorem (the subdifferential at a generic point is contained in a sphere), a generic Gâteaux differentiability result in Banach spaces of class S and a generic Fréchet differentiability result in Asplund spaces. At least two methods can be used to prove these results: first, a direct one, and second, a more general one, based on the theory of monotone operators. Since this last theory was previously developed essentially for monotone operators defined on open sets, it was necessary to extend it to the context of monotone operators defined on a larger class of sets, our "quasi open" sets. This is done in Chapter III. As a matter of fact, most of these results have an even more general nature and have roots in the theory of minimal usco maps, as shown in Chapter II.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Luxemburg, W. A. J.
Thesis Committee:
  • Luxemburg, W. A. J. (chair)
  • Aschbacher, Michael
  • Fuller, James
  • Kechris, Alexander S.
Defense Date:15 May 1989
Record Number:CaltechTHESIS:08232013-082402986
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7933
Deposited By: Benjamin Perez
Deposited On:23 Aug 2013 17:51
Last Modified:05 Jan 2022 19:06

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