MA8106 Harmonic Analysis Spring 2018
This week we meet on Monday February 26th 11:15-13:00 in Simastuen (6th floor SBII) to discuss problems for chapter 4. Then on Wednesday usual time continuing chapter 5, Thursday 10:15-12:00 in Simastuen and Friday usual time, we start chapter 7 on Thursday.
The first meeting will be on Friday, January 12th, 10:15 in KJL 21. Information about the course will be given and the schedule will be finalized. The suggested schedule is Monday/Wednesday/Friday 10.15-12.00.
The first lecture is planned for Friday, January 19th. Preliminary schedule can be also found below.
Check out this schools (if you are interested please register and send me an email):
Harmonic analysis in PCMI Summer School, deadline for application January 15th https://pcmi.ias.edu/program-index/2018
Winter school in Geilo, Norway, March 4-10, deadline for application January 4th http://serre.mat-stat.uit.no/Geilo/
Textbok and additional reading
Book: Camil Muscalu and Wilhelm Schlag, “Classical and Multilinear Harmonic Analysis", Cambridge Studies in Advanced Mathematics Vol. 137, Cambridge University Press, Cambridge, 2013
The first volume starts with classical one-dimensional topics such as Fourier series, harmonic functions, and the Hilbert transform. Then the higher-dimensional Calderón–Zygmund and Littlewood–Paley theories are developed. Probabilistic methods and their applications are discussed, as well as applications of harmonic analysis to partial differential equations. The volume concludes with uncertainty principles (chapter 10), Fourier restrictions theorems (chapter 11) an introduction to Weyl calculus (chapter 12). We plan to cover some or all of these topics.
- Y. Katznelson, An introduction to harmonic analysis. Third edition. Cambridge Mathematical Library. Cambridge University Press, Cambridge, 2004.
- E.M.Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton University Press
- A.Torchinsky, Real-variable methods in harmonic analysis, Dover Publications, Inc.
- E.M. Stein, Singular integrals and differentiability properties of functions. Princeton Mathematical Series, No. 30, 1970 (old but very nice).
- Monday, 10:15-12:00, KJL 21
- Wednesday, 8:15-10:00, B21
- Friday, 10:15-12:00, KJL 21
Lecturer : Eugenia Malinnikova
Syllabus and requirements for the examination
- The syllabus for the course is as defined by the lectures described in detail below. An oral examination will be held in May-June 2018.
Contents of the lectures
Preliminary and ambitious plan, to be updated through out the semester
|2||No lectures this week. Meeting Friday, 12.01||Read Chapter 1.1-1.3, notes||1P: 1,5,6,7,9,11,12 solution||you should know all material in 1.1-1.3, see the note for some comments and details|
|3||Lecture 1, Friday 19.01||Chapter 1.4-1.6 notes||L1: we covered 1.4.1 and 1.4.4-6.|
|4||Lectures 2-4, Monday-Wednesday-Friday, 22-26.01||Chapter 2, 2.1-2.5 notes||2P: 5,6,7,9,10||L2: 2.1-2.3, L3: problems ch1 + Marcinkiewicz interpolation theorem (1.6 + notes), L4: 2.4, 2.5 (without 2.5.5)|
|5||Lectures 5-7, Monday-Wednesday-Friday, 29.01-02.02||Chapter 3, 3.1-3.6||3Ex: 3,4; 3P: 5,7,9,10||L5: 3.3,3.4, 3.5.1-2, 3.6; L6: problems ch2, L7:3.1-3.2|
|6||Lectures 8-10, Monday-Wednesday-Friday, 5-9.02||Chapter 4, 4.1-4.3||4Ex: 4,5; 4P: 1,2,4,5,6,7||L8: 4.1.3, Nyquist density, 4.2.1 Shrodinger eq. L9: Ex ch 3, harmonic measure, problem 3.7, L10: 4.2 3,|
|7||No lectures this week||Read Chapter 5.1-5.2.1|
|8||Lectures 11-13, Monday-Wednesday-Friday , 19-23.02||Chapter 5.2||5Ex: 2,3 5: 3,5,6,8||L11: 4.2 remarks, 4.3.2 L12: problems ch3, ex ch L13: 5.2|
|9||Lectures 14-17, Monday-Wednesday-Friday, 26.02-2.03||Chapter 5.3, 7.1||L14: Problems ch 4, L15: 5.2-3, L16: 5.3, L17: 7.1|
|10||Lecture 18, Monday, 5.03||Chapter 7.2-7.3||7Ex: 1,4,6; 7P: 2||L18 7.2-7.3|
|11||Lecture 19,||Read Chapter 6.1-6.2||L19: Problems ch 5|
|12||No lectures this week||Read Chapter 6.3|
|14||Lectures 20-21, Wednesday-Friday, 4-6.04||Chapter 7.4-7.6||7Ex: 8,9; 7P: 8,10||L20: 7.4, L21:7.5-6|
|15||Lectures 22-24, Monday-Wednesday-Friday, 9-13.04||Chapter 8.1-2, 8.4||8Ex: 1,6; 8P: 2,3,7||L22: 8.1-2, L23: Problems ch7, L24: 8.4|
|16||Lectures 25-27, Monday-Wednesday-Friday, 16-20.04||Chapter 9-10||L25: 9.1, L26: 9.2, L27: 10.1-2|
|17||Lectures 28-29, Monday-Wednesday, 23-25.04||Chapter 10||L28: 10.3, L29: Problems ch7,8|