TMA4170 Fourieranalyse våren 2014

Kursbeskrivelse finnes i studiehåndboka.

Beskjeder

05.06	Exam text is here
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

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.
Week 3	here.
Week 4	here.
Week 5	here.
Week 6	here.
Week 7	here.
Week 8	27.1, 27.3 28.1, 28.2, 28.6, 28.12
Week 9	No homework
Week 10	32.5, 32,4, 32.6, 33.1, 33.3, 33.4, 34.2
Week 11	31.6, 31,7, 31.9, 31.10
Week 12	here.
Week 13	here.
Week 14	Exercises ## 1,3,4,6 from handouts

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
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