Coursebooks 2017-2018

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Harmonic analysis

MATH-405

Lecturer(s) :

Krieger Joachim

Language:

English

Summary

An introduction to methods of harmonic analysis. Covers convergence of Fourier series, Hilbert transform, Calderon-Zygmund theory, Fourier restriction, and applications to PDE.

Content

-Fourier series, convergence and summability.

-Fourier series, convergence and summability.

-Hilbert transform.

-Calderon-Zygmund theory of singular integrals.

-Liitlewood-Paley theory.

-Fourier restriction.

-Applications to dispersive PDE.

Keywords

Fourier series, convergence, singular integrals, Calderon-Zygmund theory, Fourier restriction.

Learning Prerequisites

Required courses

Analyse I - IV, Algebre lineaire I et II.

Recommended courses

Analyse I - IV, Algebre lineaire I et II.

Important concepts to start the course

Understand key concepts of real analysis, such as measure and Lebesgue integral. Be able to construct a rigorous mathematical argument.

Learning Outcomes

By the end of the course, the student must be able to:

Transversal skills

Teaching methods

Two hours ex cathedra lectures, two hours of exercises led by teaching assistant.

Expected student activities

Attend lectures and exercise sessions, read course materials, solve exercises.

Assessment methods

Oral exam at the end of course.

Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

Supervision

Office hours No
Assistants Yes
Forum No

Resources

Bibliography

-Classical multilinear harmonic analysis by C. Muscalu and W. Schlag.

-Singular integrals and differentiability properties of functions by E. Stein.

Notes/Handbook

No.

Websites

In the programs

  • Applied Mathematics, 2017-2018, Master semester 2
    • Semester
      Spring
    • Exam form
      Oral
    • Credits
      5
    • Subject examined
      Harmonic analysis
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Applied Mathematics, 2017-2018, Master semester 4
    • Semester
      Spring
    • Exam form
      Oral
    • Credits
      5
    • Subject examined
      Harmonic analysis
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Mathematics - master program, 2017-2018, Master semester 2
    • Semester
      Spring
    • Exam form
      Oral
    • Credits
      5
    • Subject examined
      Harmonic analysis
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Mathematics - master program, 2017-2018, Master semester 4
    • Semester
      Spring
    • Exam form
      Oral
    • Credits
      5
    • Subject examined
      Harmonic analysis
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Mathematics for teaching, 2017-2018, Master semester 2
    • Semester
      Spring
    • Exam form
      Oral
    • Credits
      5
    • Subject examined
      Harmonic analysis
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks
  • Mathematics for teaching, 2017-2018, Master semester 4
    • Semester
      Spring
    • Exam form
      Oral
    • Credits
      5
    • Subject examined
      Harmonic analysis
    • Lecture
      2 Hour(s) per week x 14 weeks
    • Exercises
      2 Hour(s) per week x 14 weeks

Reference week

MoTuWeThFr
8-9
9-10
10-11
11-12
12-13 MAA110
13-14
14-15 MAA110
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Lecture
Exercise, TP
Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German