# TMA4170 Fourieranalyse våren 2014

Kursbeskrivelse finnes i studiehåndboka.

## Beskjeder

 05.06 Exam text is here Exam solutions (preliminary) are here Next office hour/ preexam meeting: 02.06.2014, 11:15-13:00. My office As was promised: One of the homework assignments will be literally included intio final exam (: Nearest office hour: 26.05.2014, 13:00-14:30 in my office. More office hours to be announced later Nearest office hour: 19.05.2014, 10:00 in my office. More office hours to be announced later 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 Nearest office hour: 12.05.2014, 10:00 in my office. More office hours to be announced later Final pensum is here 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 The homework for week: Reetition ofthe Fourier transform: 31.6, 31.7, 31.9,31.10 The homework for week 10: 32.4, 32.5, 32.6. 33.3, 33.4 The homework for this week: 27.1, 27.3 28.1, 28.2, 28.6, 28.12 Lecture 14 on 20.02.2014: Lessons 29 - 30 of the textbook Lecture 13 on 18.02.2014: Lessons 26 - 28 of the textbook Plans of the Lectures 11 and 12 can be found here and here The homework for this week is here. The homework for this week is here. The homework for this week is here, Lecture 08 of 04.02 can be found here. It includes mailnly Lesson 17 from the textbook. 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. The homework for this week is here. The protocol of the Lecture 05 can be found here Tentative plan for todays and the nearest lectures is here The protocol of the Lectures 03 and 04 can be found here and here The home assignment for week 3 can be found here. Homework for this week will be posted on Sunday after my return to Trondheim. I apologize for the delay The home assignment for week 2 can be found here. New rooms have been assigned for our course, see kursinformasjon The protocol of the Lecture 02 can be found here Tentative plan for todays and the nearest lectures is here Tomorrow lecture will take place in room 734 SB2, as yestarday The protocol of the Lecture 01 can be found at http://www.math.ntnu.no/emner/TMA4170/2014v/Lectureplans/Lecture01Fourier.pdf The first lecture will take place on 07.01

## Kursinformasjon

#### LECTURES

• Tuesday 14.15-16, Auditorium R30
• Thursday 10.15-12, Auditorium MA23
• Exam date: June, 03

### 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.
 Week 2 here. here. here. here. here. here. 27.1, 27.3 28.1, 28.2, 28.6, 28.12 No homework 32.5, 32,4, 32.6, 33.1, 33.3, 33.4, 34.2 31.6, 31,7, 31.9, 31.10 here. here. Exercises ## 1,3,4,6 from handouts

### 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 Selfadjoint Sturm Louville operators, eigenfunction expansions Lessons 8-9 Lessons 11 -14 (short overview) Lessons 15-16 Lessons 17-23 Application to random walks Lessons 26-30 Lessons 31 - 33 Lessons 34 -35 Lessons 36-38 lessons 41-42

## Referansegruppe

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