Coursebooks

Distribution and interpolation spaces

MATH-502

Lecturer(s) :

Radici Emanuela

Language:

English

Summary

The aim of this course is to provide a solid foundation of theory of Distributions, Sobolev spaces and an introduction to the more general theory of interpolation spaces.

Content

After a brief review on weak topologies and other tools from functional analysis, we will introduce the concept of distribution and Fourier transform and we will pass then to the definition of Sobolev spaces (first in the scalar then in the multidimensional setting). We will discuss preliminary results on Sobolev spaces, such as approximation results, extension operators, and the Sobolev immersions. Finally, we will introduce the theory of interpolation spaces as a generalization of Sobolev spaces.

Keywords

Distributions, Sobolev Spaces, Interpolation Spaces

Learning Prerequisites

Required courses

Basic courses of analysis 

Recommended courses

Functional analysis 

Learning Outcomes

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

Assessment methods

Written

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

Assistants Yes

Resources

Moodle Link

In the programs

Reference week

 MoTuWeThFr
8-9  MXG110  
9-10    
10-11  MXG110  
11-12    
12-13     
13-14     
14-15     
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