Introduction to Functional Analysis — FUN

Instructor: Dr. Dát&vid KUNSZENTI-KOVÁCS

Text:  A Course in Functional Analysis, by John Conway, Springer 2007

Prerequisites: calculus and linear algebra

Course description: The course provides an introduction to functional analysis. Only some knowledge of calculus and linear algebra is assumed. As an application we will discuss the foundations of quatum mechanics at the end of the course.

Topics:

Normed spaces, Banach spaces: standard examples of function spaces, bounded linear operators, linear functionals, dual spaces and weak topologies

Hilbert spaces: inner products, orthogonal complements, representation of linear functionals, adjoint operator, self-adjoint, unitary and normal operators.

Fundamental theorems of functional analysis: Hahn-Banach theorem, Uniform Boundedness Theorem, Open Mapping Theorem, Closed Graph Theorem.

Spectral theory: resolvent and spectrum, bounded self-adjoint operators, compact operators.

Unbounded linear operators and applications to PDE theory.