Introduction to spectral theory of unbounded operators

par Hatem Najar (Université de Monastir - Tunisie & Taibah University (KSA))

Slides : najarcimpa2016.pdf (1.35 Mo) in english.
ce cours sera donné en français

Abstract: This course introduce to the operator theory, basic spectral theory for unbounded operators and their use in quantum theory. The central mathematical tool of this course is the spectral theory of self-adjoint operators. The course is for audience from graduate students, PhD students and young researchers.
Details: Basic definitions on Banach and C*-algebra of operators, notion of spectrum and resolvent, von Neumann series theorem, spectral radius formula; Riesz projector, closed and closable operators, the adjoint, criterion for self-adjointness and for essential self-adjointness. Unbounded operators on Hilbert spaces: Laplacian operator, perturbation theory and self-adjoiness, Shrödinger operators...