The take home exam can be retrieved at the expedition on the fourth floor (femte vĂ¥ningen). The solved problems shall be returned before January 17, 2020.

To recieve a pass in the oral exam one should do well on the following repetition questions.

Renardy and Rogers is available on the net from LU computers.

Lecture notes will be handed out during the course together with exercises.

In Mathematical structures there are background material to parts of the course.

Week | Content. Section in RR |
---|---|

1 | Introduction. 6.1. |

1 | Banach and Hilbert spaces. 6.1. |

2 | Hilbert space geometry. 6.1.3, 6.3.1, 6.3.2. |

3 | Basis. 6.2.1, 6.2.2. |

3 | Weierstrass approximation. 6.2.3, 2.3.3. |

4 | Dual spaces, Hahn-Banach. 6.3.1, 6.3.2, 6.3.3. |

5 | Weak convergence, uniform boundedness. 6.3.4, 6.3.5. |

5 | Sobolev spaces. 7.1. |

6 | Fourier transform, Sobolev imbedding theorem 7.2.2. |

7 | Sobolev imbedding theorem 7.2.3. |

1 | Compactness, continuity. |

2 | Operator theory 8.1. |

4 | Spectral theory 8.3. |

5 | Selfadjointness 8.4, Repetition. |

Sheets with exercises will be handed out during the course.

The exercises are discussed during the exercise sessions every second Friday.

- Exercises September 3
- Exercises September 6
- Exercises September 10
- Exercises September 17
- Exercises September 20
- Exercises September 24
- Exercises October 1
- Exercises October 4
- Exercises October 8
- Exercises October 15
- Exercises October 22
- Exercises November 4
- Exercises November 18
- Exercises December 2

To recieve a pass in the oral exam one should do well on the following repetition questions.

Tuesday 10-12 and Friday 13-15 in MH 333 (see timeedit).

The following are three books on functional analysis which are free on the net.

- A course on functional analysis by Gerald Teschl
- Applied analysis by John Hunter and Bruno Nachtergaele.
- Linear functional analysis by W. Chen.

Functional analysis and harmonic analysis are fundamental tools in many important areas of abstract and applied mathematics as well as mathematical statistics and numerical analysis. The aim of the course is to convey knowledge about basic concepts and methods, and to give the ability, both to follow discussions where these are used and to independenty solve mathematical problens which arise in the applications. An important goal of the course is also to develop a power of abstraction which makes it easier to see analogies between problems from apperntly different fields.

- Lecturer:
- Pelle Pettersson
- Time:
- Lp 1 and 2 autumn 2018
- Duration:
- Lectures 28 h and problem sessions 28 h.
- Code:
- FMAN80 (FMAN80F).
- Points:
- 7.5.
- Literature:
**Renardy and Rogers**:*An introduction to Partial Differential equations*, Second edition, Springer.