# TMA4170 Fourieranalyse våren 2014

Kursbeskrivelse finnes i studiehåndboka.

## Beskjeder

05.06 | Exam text is here |
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03.06 | Exam solutions (preliminary) are here |

26.05 | Next office hour/ preexam meeting: 02.06.2014, 11:15-13:00. My office |

19.05 | As was promised: One of the homework assignments will be literally included intio final exam (: |

19.05 | Nearest office hour: 26.05.2014, 13:00-14:30 in my office. More office hours to be announced later |

14.05 | Nearest office hour: 19.05.2014, 10:00 in my office. More office hours to be announced later |

11.05 | Aids on exams: One A4-sized sheet of paper stamped by the Department of Mathematical Sciences and written form one side; HP30S or Citizen SR-270X |

07.05 | Nearest office hour: 12.05.2014, 10:00 in my office. More office hours to be announced later |

05.05 | Final pensum is here |

16.03 | Lecture plan for this week: Tuesday 11.03: Application to random walks, see notes;Thursday 14.03: Short time Fourier transform, see Sectiona 3.1 and 3.2 of the notes below |

16.03 | The homework for week: Reetition ofthe Fourier transform: 31.6, 31.7, 31.9,31.10 |

10.03 | The homework for week 10: 32.4, 32.5, 32.6. 33.3, 33.4 |

22.02 | The homework for this week: 27.1, 27.3 28.1, 28.2, 28.6, 28.12 |

21.02 | Lecture 14 on 20.02.2014: Lessons 29 - 30 of the textbook |

19.02 | Lecture 13 on 18.02.2014: Lessons 26 - 28 of the textbook |

16.02 | Plans of the Lectures 11 and 12 can be found here and here |

16.02 | The homework for this week is here. |

09.02 | The homework for this week is here. |

02.02 | The homework for this week is here, Lecture 08 of 04.02 can be found here. It includes mailnly Lesson 17 from the textbook. |

29.01 | Lecture 06 of 23 and 28.01 covers lessons 8 and 9 of the textbook. We studied the Discrete Fourier Transform and Fast Fourier Transform. The plan of the Lecture 07 of 30.01 can be found here. This lecture contains a survey of Chapter IV of the textbook about the Lebesgue integral. |

26.01 | The homework for this week is here. |

25.01 | The protocol of the Lecture 05 can be found here |

21.01 | Tentative plan for todays and the nearest lectures is here |

19.01 | The protocol of the Lectures 03 and 04 can be found here and here |

19.01 | The home assignment for week 3 can be found here. |

16.01 | Homework for this week will be posted on Sunday after my return to Trondheim. I apologize for the delay |

11.01 | The home assignment for week 2 can be found here. |

09.01 | New rooms have been assigned for our course, see kursinformasjon |

09.01 | The protocol of the Lecture 02 can be found here |

09.01 | Tentative plan for todays and the nearest lectures is here |

08.01 | Tomorrow lecture will take place in room 734 SB2, as yestarday |

07.01 | The protocol of the Lecture 01 can be found at http://www.math.ntnu.no/emner/TMA4170/2014v/Lectureplans/Lecture01Fourier.pdf |

06.01 | The first lecture will take place on 07.01 |

## Kursinformasjon

#### LECTURES

### Teacher

- Yurii Lyubarskii: Office 954 in SB II, yura@math.ntnu.no

Please write TMA4170 in the subject line on all e-mail related to the course.

Office hours: Monday 13:15-14:00

#### LECTURE PLANS

- Lecture 01 (07.01.2014)
- Lecture 02 (09.01.2014)
- Lecture 03 (14.01.2014)
- Lecture 04 (16.01.2014)
- Lecture 05 (21.01.2014)
- Lecture 06 (23.01.2014 and 28.01.2014) covers lessons 8 and 9 of the textbook. We studied the Discrete Fourier Transform and Fast Fourier Transform.
- Lecture 07(30.01.2014): This lecture contains a survey of Chapter IV of the textbook about the Lebesgue integral.
- Lecture 08 (04.02,2014): It includes mailnly Lesson 17 from the textbook.
- Lecture 09 (06.02.2014): Lesson 18 from the textbook
- Lecture 10 (11.02,2014).
- Lecture 11 (13.02.2014)
- Lecture 12 (18.02.2014)
- Lecture 13 (18.02.2014): Lessons 26 - 28 of the textbook
- Lecture 14 (20.02.2014): Lessons 29 - 30 of the textbook
- Lecture 15 (25.02.2014): Lesson 31 of the textbook
- …. to be filled ….

- Lecture (11.03.2014): Application to random walks, see notes
- Lecture (13.03.2014): Short time Fourier transform, see Sections 3.1 and 3.2 of the notes
- Lecture (18.03.2014): Wavelet transform see notes below
- Lecture (20.03.2014): Wavelet transform, continuation
- Lecture (25.03.2014): Elements of Gabor analysis see notes below
- Lecture (27.03.2014): Elements of Gabor analysis continuation. Elemets of frame theory (notes come later on)
- Lecture (01.04.2014): Frame operators for Gabor systerms (notes come later on).Beginning of Haar wavelet analysis (see handouts)
- Lecture (03.04.2014):Haar wavelet analysis (see handouts)

#### EXERCISES

- Will be discussed on Tuesdays after the lectures.

### Notes

### Literature

Main textbooks * "Fourier Analysis and Applications" by G. Gasquet & P. Witomski, Springer. * "Fourier series and integrals" by H.Dym, H.P.McKean, H. P., Academic Press. Auxiliary * "A Guide to Distribution Theory and Fourier Transforms" by R. Strichartz, World Scientific.--Easy to read. Useful information. * "A First Course on Wavelets with Fourier Analysis" by A. Boggeness, F. Narcowich, Prentice Hall.--An accessible introduction to wavelets (the Fourier Analysis is not well presented). * "Wavelets -A Primer" by Ch. Blatter * "Fourier Series and Orthogonal Functions" by H. Davis, Dover. Clear examples and good proofs. (No wavelets.)

## (Very) Tentative plan

##### according gasquet and witomski (some lessons will be just partially included in the course)

Ch. 2 | Lessons 3-7 |
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Addition | Selfadjoint Sturm Louville operators, eigenfunction expansions |

Ch.3 | Lessons 8-9 |

Ch.4 | Lessons 11 -14 (short overview) |

Ch.5 | Lessons 15-16 |

Ch.6 | Lessons 17-23 |

Addition | Application to random walks |

Ch.8 | Lessons 26-30 |

Ch.9 | Lessons 31 - 33 |

Ch.10 | Lessons 34 -35 |

Ch.11 | Lessons 36-38 |

Ch.12 | lessons 41-42 |

## Referansegruppe

- Herman Galteland, hermanga@stud.ntnu.no
- Christian Jakobsen, crijak@stud.ntnu.no
- Trygve Aune, trygvinhu@gmail.com