Department of Mathematics

Lecturer	Sameh TAMRABET
Information	Master - Applied Mathematics Department of Mathematics Website : https://www.univ-soukahras.dz/en/module/944 Semester : S2 Unit : UEF2 Credit : 9 Coefficient: 4
Content	1- Reminders about bounded operators Definition and examples, bounded linear operators, sum and product of operators, inverse operator, self-adjoint operator, orthogonal projection operators, spectrum of an operator, spectral radius, resolvent. 2. Introduction to unbounded operators Closed operator, adjoint of an operator, symmetric operators, self-adjoint operators, self-adjoint extensions of a symmetric operator, resolvent set and spectrum 3. Compact or compact resolvent operators. Notions of compactness and weak convergence, spectral theory of compact self-adjoint operators, spectral decomposition of a compact self-adjoint operator, spectral decomposition of a self-adjoint operator with compact resolvent, singular value decomposition of a compact operator , Picard\'s theorem and applications, Courant-Fisher\'s Min-Max principle.
Evaluation	33% (continu) + 67% (examen)