Henrik Shahgholian (KTH)                           Salvador Rodriguez-Lopez  (SU) 

henriksh@math.kth.se                                 s.rodriguez-lopez@math.su.se

Lectures and exercise sessions:

First lecture starts on Friday 13:15--15:00, 31 August. 

PART I:

Lectures 1--8:  Fridays  13:15--15:00,   KTH,  Lindstedtsv. 22, room F11                

August 31, Sept. 7, 14, 21, 28, Oct. 5, 12, 19

Exercise sessions: (by Dr. Andreas Minne)  Wednesdays  13:15--15:00,  KTH,  

Sept.5: L21, Sept.12: L44, Sept.19: L21,  Sept.26: D35, Oct. 3: D32, Oct. 10: D35,   Oct. 17: D32,  

Oct. 24  K53

PART II:

Classes for PART 2 will take place at kräftriket SU: Building 6, rum 306.

Lectures 9--14:  Fridays 13:15--15:00,  Nov.  2, 9, 16, 23, 30, Dec.  7, (Possibly an extra lecture on Dec.14) 

Exercise sessions:  Fridays 15:15-17:00   

Language:    

English

Topics:

Part 1:                    

Measure, Integration and Applications (6+2 lectures):

Webpage:  click HERE                       

Part 2:

Functional Analysis and Applications (5+1 lectures):

Webpage:  click HERE Links to an external site.

Prerequisites:  

Foundations of Analysis SF2713, or equivalent.

Literature:  

A. Friedman, Foundations of Modern Analysis, Dover 1982

Goal:

To learn basics of advanced real analysis, such as the notion of measure, Lebesgue integral, and certain convergence aspects. Basics of functional analysis such as Banach spaces and linear operators will be introduced.

These concepts will then be looked at from an application point of view, that may includesome of these topics: Fourier analysis, Ergodic theory, Probability theory, Sobolev spaces, Partial Differential equations. After completing the course the students are expected to:

i)    Be familiar with concepts in measure, integration, and operator theory,

ii)   Be able to state and prove basic theorems in measure and operator theory,

iii)  Be able to use methods from above within applications.