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Hille-Yosida theory in convenient analysis.

Josef Teichmann (2002)

Revista Matemática Complutense

A Hille-Yosida Theorem is proved on convenient vector spaces, a class, which contains all sequentially complete locally convex spaces. The approach is governed by convenient analysis and the credo that many reasonable questions concerning strongly continuous semigroups can be proved on the subspace of smooth vectors. Examples from literature are reconsidered by these simpler methods and some applications to the theory of infinite dimensional heat equations are given.

How to define "convex functions" on differentiable manifolds

Stefan Rolewicz (2009)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In the paper a class of families (M) of functions defined on differentiable manifolds M with the following properties: 1 . if M is a linear manifold, then (M) contains convex functions, 2 . (·) is invariant under diffeomorphisms, 3 . each f ∈ (M) is differentiable on a dense G δ -set, is investigated.

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