The take home exam can be retrieved at the expedition on the fourth floor (femte våningen). The solved problems shall be returned before January 18, 2019.

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.

- Exercises September 4
- Exercises September 7
- Exercises September 11
- Exercises September 18
- Exercises September 21
- Exercises September 25
- Exercises September 26
- Exercises September 29
- Exercises October 9
- Exercises October 16
- Exercises October 19
- Exercises November 5
- Exercises November 12

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.

The course is intended to be taken together with the course Partial differential Equations with Distribution Theory, FMA 250, (using the same course literature), but can without problems be read as a standalone course.

- Lecturer:
- Pelle Pettersson
- Time:
- Lp 1 and 2 autumn 2018
- Duration:
- Lectures 28 h and problem sessions 28 h.
- Code:
- FMAN80 (FMA260Fny).
- Points:
- 7.5.
- Literature:
**Renardy and Rogers**:*An introduction to Partial Differential equations*, Second edition, Springer.