# TMA4170 Fourieranalyse våren 2016

Kursbeskrivelse finnes i studiehåndboka.

## Beskjeder

*NO EXERCISE SESSION TUESDAY 12.I.*

No lectures on week 1
* THE FIRST LECTURE WILL TAKE PLACE ON MONDAY THE 11th of January
* THE FIRST EXERCISE ON TUESDAY the 19th *

## Kursinformasjon

#### LECTURES

• Monday 10.15-12, Auditorium KJL24
• Friday 14.15-16, Auditorium KJL24

#### EXAM.

• Exam date: Friday, June 16th.
• PERMITTED AIDS: One A-4 sized sheet of yellow paper stamped by the Department of Math. Sciences (on it you may in advance write whatever pleases you).
• 16.V.2015 Text
• 16.V.2015 Solutions

#### SYLLABUS

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
• all the EXERCISES!

___

#### EXERCISES

• Tuesday 17.15-18, KJL24.

#### TEXT BOOK

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 book is too weak when it comes to some proofs).

### Teacher

• Peter Lindqvist: Office 1152 in SB II, lqvist@math.ntnu.no
Please write TMA4170 in the subject line on all e-mail related to the course.
• Office hours: ???day 1?:15-1?:00

#### EXERCISES

This is from 2015 and will gradually be updated.

 Week 3 Week 4 Exercises Text lost now Exercises Exercises Exercises Exercises Misprint: multiply dr by r in ex. 3 Exercises Exercises Some helpdistribution.pdf Exercises Laplace Eqn Exercises Ex. 2, misprint: square the norm. (use Thm for orthonorm. of translates) Chapter V: 3,4,6,17,18 Exercises Moved to April 10th. Obvious missprint in the range of integration of the Four.coeff. See week 13 Exercises Extra Exercises Compensates 27.III. Second part of 7 Solution?! In 9 misprint

### Notes

• 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
• "Fourier Series and Orthogonal Functions" by H. Davis, Dover. Clear examples and good proofs. (No wavelets.)

## Tentative lecture plan

===usually according to Boggess & Narcowich===

 Ch. 0 Ch 1 Ch 2 Week 2 The Hilbert Space. Orthonormal bases. Fourier Coefficients. The Trigonometric System. Week 3 Convergence. Dirichlet's Kernel, Fejer's Kernel. Gibb's Phenomenon week 4 (Parseval's formula Ch 1), The Fourier Transform week 5 Fourier transform in L2, Plancherel's formula, convolutions. Sampling Theorem. week 6 Oversampling. Heisenberg's Principle. Poisson's summation formula. ——–7 Discrete Fourier Transform. week 8 Fast Fourier Transform. Theory of Distributions Not in the text book. week 9 Fourier Transform of Distributions. The Schwartz class. Haar basis not in the text book. week 10 Haar Basis. Wavelets. week 11 Wavelets. week 13 Daubechies' Wavelets. Shannon's Wavelet Calculation of 2nd moment Last 5 lines irrelevant. One 1/2 missing inside Q(w) week 14 Continuous Wavelet Transform. Battle-Lemarie wavelet week 15 Equidistributed numbers, various things, Repetition week 16 Repetition week 17 ???

## Referansegruppe

• N. N.* * ???@stud.ntnu.no
• N. N. * * ???@stud.ntnu.no ?
• N. N.