### Instruction

Name | Cr | Method of study | Time | Location | Organiser |
---|---|---|---|---|---|

Spectral theory | 10 Cr | Lecture Course | 13.1.2020 - 30.4.2020 |

Name | Cr | Method of study | Time | Location | Organiser |
---|---|---|---|---|---|

Spectral theory | 10 Cr | Lecture Course | 16.1.2018 - 20.3.2018 |

### Target group

Optional course.

Master's Programme in Mathematics and Statistics is responsible for the course.

The course belongs to the Mathematics and Applied mathematics module.

The course is available to students from other degree programmes.

### Prerequisites

B.Sc.-level mathematics, Functional analysis

### Learning outcomes

Knowledge of basic spectral theory for bounded and unbounded operators in Hilbert spaces and applications to partial differential equations

### Timing

Recommended time/stage of studies for completion: 1. or 2. year

Term/teaching period when the course will be offered: varying

### Contents

Unbounded operators in Hilbert spaces; closed, symmetric and self-adjoint operators; spectral theorem; perturbation theory; applications to elliptic PDE

### Activities and teaching methods in support of learning

Lectures and exercise classes

### Study materials

Required: lecture notes.

Recommended: Reed-Simon, Methods of modern mathematical physics; Davies: Spectral theory and differential operators

### Assessment practices and criteria

Exam and excercises, Course will be graded with grades 1-5

### Recommended optional studies

Sobolev space theory, Fourier analysis, theory of distributions

### Completion methods

Exam, other methods will be described later