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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the second derivatives of convex functions on Hilbert spaces


Author: Nobuyuki Kato
Journal: Proc. Amer. Math. Soc. 106 (1989), 697-705
MSC: Primary 47H05; Secondary 46G05, 58C20
MathSciNet review: 960646
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Abstract: Let $ \phi $ be a proper l.s.c. convex function on a real Hilbert space $ H$. We show that if $ H$ is separable, then $ \phi $ is twice differentiable in some sense on a dense subset of the graph of $ \partial \phi $.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0960646-4
PII: S 0002-9939(1989)0960646-4
Keywords: Convex function, subdifferential, second derivative, convergence in the sense of Mosco
Article copyright: © Copyright 1989 American Mathematical Society