Introduction to Functional Analysis — FUN

Instructor: Dr. Maté MATOLCSI

Text:  Introductory Functional Analysis with Applications, by Erwin Kreyszig (Wiley, 1989)

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.

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 , finite dimensional case, bounded self-adjoint operators, compact operators.

Unbounded linear operators and the foundations of quantum mechanics.