A primary introduction to spectral theory

Doctoral Course, Novembre 2019

LAGA, Université Paris 13. Site de Villetaneuse. Room B407 Access
By Jianwei Yang (International Chair of the Labex MME-DII)

Schedule

Contact

yang arrobas math.univ-paris13.fr

Abstract

This course will be at very elementary level with prerequisite only on limited knowledge of integration theory and linear algebra. We will start with the theory of Hilbert space and operators on it, focusing our attention on self-adjoint operators and compact operators. After introducing the general notion of spectrum of an operator and its classification, we move on to certain properties of these operators in connection with their spectral behavior, including a simple version of the Fredholm alternative and Weyl's theorem, which is about the invariance of the essential spectrum of an operator under relatively compact perturbation. Finally, we will present an application of the Weyl theorem to an up-to-date research (joint with professor Duyckaerts) concerning the determination of the essential spectrum of a linearized operator, arising as a sum of the Laplace operator and a potential equipped with several properties.

Written notes

Available here


LOGO MME-DII