Analyse hilbertienne pour le traitement des données

Objectives

Hilbert spaces are instrumental for solving problems whose unknown is a function. They are used for solving PDE’s when the spectral method is concerned. They provide also a powerful framework for Fourier and Wavelet decomposition. Finally separations results are essential for many convex machine-learning algorithms. The goal of the course is to provide a rigorous exposition of these concepts, and to illustrate them on practical examples from PDE’s and signal processing.

Bibliography

- Une exploration des signaux en ondelettes, S. Mallat, Les Editions de l’Ecole Polytechnique, 2000
- Analyse réelle et complexe : Cours et exercices, W. Rudin

Pre-requisites

Linear algebra

Session 1 ou session unique - Contrôle des connaissances

Session 2 - Contrôle des connaissances