The search session has expired. Please query the service again.
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.
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.
Download Results (CSV)