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Norm-attaining polynomials and differentiability

Juan Ferrera — 2002

Studia Mathematica

We give a polynomial version of Shmul'yan's Test, characterizing the polynomials that strongly attain their norm as those at which the norm is Fréchet differentiable. We also characterize the Gateaux differentiability of the norm. Finally we study those properties for some classical Banach spaces.

Inf-convolution and regularization of convex functions on Riemannian manifolds of nonpositive curvature.

Daniel Azagra;  Juan Ferrera — 2006

Revista Matemática Complutense

We show how an operation of inf-convolution can be used to approximate convex functions with C smooth convex functions on Riemannian manifolds with nonpositive curvature (in a manner that not only is explicit but also preserves some other properties of the original functions, such as ordering, symmetries, infima and sets of minimizers), and we give some applications.

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