TMA4170 Fourieranalyse våren 2016
Kursbeskrivelse finnes i studiehåndboka.
OFFICE HOURS MONDAY 6 JUNE 15-16, TUESDAY 7 JUNE 14-16 IN 1152 SB II
*Extra exercises during the lecture Monday 25.IV.2016*
* THE FIRST LECTURE WILL TAKE PLACE ON MONDAY THE 11th of January 2016
* THE FIRST EXERCISE SESSION ON TUESDAY the 19th of January 2016
- Monday 10.15-12, Auditorium KJL24
- Friday 14.15-16, Auditorium KJL24
- Tuesday 17.15-18. Auditorium KJE24
From the book by Boggess& Narcowich
- Chapter 1
- Chapter 2
- Section 3.1
- Chapter 4
- Chapter 5
- Chapter 6
- Section 7.4
Moreover, the syllabus contains:
- the Fourier Transform of Distributions
- the Poisson Summation Formula
- the Fourier Transform in several variables (basic knowledge). Radial functions.
- all the EXERCISES!
Most of the material will be found in
A. Boggess & F. Narcowich: A first course in Wavelets with Fourier Analysis.
The Fourier Series and Transforms have to be complemented with other sources. The Fourier transforms of distributions have to be added.
- Peter Lindqvist: Office 1152 in SB II, lqvist [at] math [dot] ntnu [dot] no
Please write TMA4170 in the subject line on all e-mail related to the course.
- Office hours: ???day 1?:15-1?:00
|Week 3||Exercises||2016 Example 5 postponed|
|week 6||Exercises||2016. Do example 5 for many functions|
|week 8||Exercises||2016 MOVED TO G038 23.II.2016|
|week 9||Exercises||2016. Some helpdistribution.pdf. .Sign(x)|
|week 10||Exercises||2016. Not related to the examples:Laplace Eqn|
|week 11||Exercises||2016. Some solutions Appendix: some formulas in several variables|
|week 14||Chapter V: 4,5,7,8,18||2016 See Shannon's wavelet below!|
|week 15||Exercises||2016. Obvious missprint in the range of integration of the Four.coeff.ex.4|
|week 17||Extra exercises||Monday 25.IV.2016, 10-12 o"clock.|
|week 17||Exercises||Tuesday 26th of April|
More "advanced" theory:
- E. Stein, R. Shakarchi: "Fourier Analysis", Princeton.
- "A Guide to Distribution Theory and Fourier Transforms" by R. Strichartz, World Scientific.–Easy to read. Useful information.
- "Wavelets -A Primer" by Ch. Blatter
Tentative lecture plan
usually according to Boggess & Narcowich
|Week 3||Ch. 0||The Hilbert Space. Orthonormal bases. Fourier Coefficients. The Trigonometric System.Bessel's ineq.|
|Week 4||Ch 1||Convergence. Dirichlet's Kernel, Fejer's Kernel||Se notes on conv. below!|
|week 5||Ch 2||(Parseval's formula Ch 1), Gibb's phenomenon. Fourier transform|
|week 6||Ch 2||Fourier transform in L2, Plancherel's formula, convolutions. Sampling Theorem.|
|week 7||Ch 2||Oversampling. Heisenberg's Principle. Poisson's summation formula.||Exercise 2.14 Oversampling|
|——–7||Ch 3||Discrete Fourier Transform.|
|week 8||Ch 3||Fast Fourier Transform. Theory of Distributions||Not in the text book.|
|week 9||Notes||Fourier Transform of Distributions. The Schwartz class. Haar basis||not in the text book.|
|week 10||Ch 4||Haar Basis. Wavelets.|
|week 11||Ch 5||Wavelets.|
|week 13||Ch 6||Daubechies' Wavelets. Shannon's Wavelet||Calculation of 2nd moment Last 5 lines irrelevant. One 1/2 missing inside Q(w)|
|week 14||Ch 6||Daubechies's wavelet. Continuous Wavelet Transform.|
|week 15||…||Random walks, various things, H. Weyl's theorem (from the book by Stein-Shakarchi)|
|week 17||…||Extra exercises on Monday the 25.IV.2016|
- Erik Jørgensen ….. firstname.lastname@example.org
- Are Austad ….. email@example.com