Spaces of distributions of non-integer order and applications

Mardi 12 décembre 2017 14:00-15:00 - Marin Mišur - Université de Zagreb

Résumé : In this talk, we review the notion of the order of a distribution and extend it to the case of positive real numbers.
The first part of the talk is about the functional-analytic properties of the Hölder test function spaces and its duals.
Of particular interest are the C^{0,\alpha+}_c(\Omega) and the \mathcal D’_{\alpha+}(\Omega) spaces which have notably better properties such as reflexivity, compared to classical Hölder spaces.
Next, we give a few examples of distributions of fractional order.
As an application of our results, using results and tools from classical Fourier analysis, we give (in a certain sense) sharp estimates on the order of distributions which are the Fourier transform of L^p functions for p > 2.
The results presented here can easily be extended to the case of differentiable manifolds and de Rham’s currents.
This is joint work with Ljudevit Palle (Christian-Albrechts-Universität zu Kiel).

Lieu : Salle 113-115 (Bâtiment 425)

Spaces of distributions of non-integer order and applications  Version PDF