Hilbert Spaces: Introduction, basic concepts. Bounded Operators: Operators in Hilbert spaces. Definitions, properties. Bilinear forms. Operator norm. Adjoint of an operator. Self-adjoint, normal, unitary operators. Projections: Orthogonal projections, properties. Invariant subspaces. Compact Operators: Finite rank operators, compact and self-adjoint compact operators. Spectral theory: Spectral theorem for self-adjoint compact operators. Applications to integral operators and Sturm-Liouville systems. Green s functions. Operators in Banach spaces: The adjoint operator, compact operators. Fredholm Operators: Definitions, properties, Fredholm index. Unbounded Operators: Closed operators, symmetric and self-adjoint operators.
- Teacher: Νικόλαος Παπαγεωργίου
ECTS : 5
Language : el