Kaisa_2012_3_photo by Veikko Somerpuro

## Hans-Olav Tylli

Julkaistu, 31.1.2018 klo 14:22

## Hans-Olav Tylli

Julkaistu, 17.1.2018 klo 14:57

I have linked model solutions for the 1. partial exam from 27.10.2017 to the "Tehtävät"-part (I seem to have forgotten to do this earlier).

## Hans-Olav Tylli

Julkaistu, 9.1.2018 klo 15:54

The results from the course have now been linked to the page Results/Tulokset. Please note that you will have to log in to view the page.

## Hans-Olav Tylli

Julkaistu, 9.1.2018 klo 11:53

Model solutions to the 2. partial exam from 18.12.2017 have been added to the "Tehtävät"-part. Results from the course will be linked in a moment.

## Hans-Olav Tylli

Julkaistu, 15.12.2017 klo 16:59

Model solutions to the 2. partial exams from 2010 and 2008 have been linked to the course page (two different pdf-files).

## Hans-Olav Tylli

Julkaistu, 14.12.2017 klo 21:13

REMINDER: the 2. partial exam of Functional Analysis is on Monday 18.12. from 12-15 o'clock in room D123. Topics of the exam: chapters 5-9, but excluding the part "Sobolev spaces" (pp. 101-114 in the Finnish course notes).
Older partial exams (2010 and 2008), as well as a couple of final exams, have been linked to the course pages. Related model answers will be linked on Friday 15.12 (as well as for Exercises 13).
The next final exam (for the whole course) is on Wed 10.1.2018. Note that you need to register in WebOodi for final exams (at latest 10 days before the date)!

## Hans-Olav Tylli

Julkaistu, 11.12.2017 klo 20:12

A misprint has been corrected in the definition in Exercise 13:2, where the duality c_0^* = \ell^1 refers to the identification from Exercise 12:3.

## Hans-Olav Tylli

Julkaistu, 8.12.2017 klo 19:24

Exercises 13 for Wed 13.12 have been added. This is the last exercise.

## Hans-Olav Tylli

Julkaistu, 2.12.2017 klo 20:30

Solutions to Exercises 11 have been added (including an second proof of problem 11:5 that does not use the Baire theorem).

## Hans-Olav Tylli

Julkaistu, 1.12.2017 klo 15:26

Exercises 12 for Thursday 7.12 (14-16 o'clock, room C123) have been added. Note the change of day (because of Independence day 6.12 on Wednesday).

## Sivut

### Aikataulu

Tästä osiosta löydät kurssin opetusaikataulun. Tarkista mahdolliset muut aikataulut kuvauksesta.

PäivämääräAikaOpetuspaikka
Ma 4.9.2017
10:15 - 12:00
Ti 5.9.2017
12:15 - 14:00
Ma 11.9.2017
10:15 - 12:00
Ti 12.9.2017
12:15 - 14:00
Ma 18.9.2017
10:15 - 12:00
Ti 19.9.2017
12:15 - 14:00
Ma 25.9.2017
10:15 - 12:00
Ti 26.9.2017
12:15 - 14:00
Ma 2.10.2017
10:15 - 12:00
Ti 3.10.2017
12:15 - 14:00
Ma 9.10.2017
10:15 - 12:00
Ti 10.10.2017
12:15 - 14:00
Ma 16.10.2017
10:15 - 12:00
Ti 17.10.2017
12:15 - 14:00
Ma 30.10.2017
10:15 - 12:00
Ti 31.10.2017
12:15 - 14:00
Ma 6.11.2017
10:15 - 12:00
Ti 7.11.2017
12:15 - 14:00
Ma 13.11.2017
10:15 - 12:00
Ti 14.11.2017
12:15 - 14:00
Ma 20.11.2017
10:15 - 12:00
Ti 21.11.2017
12:15 - 14:00
Ma 27.11.2017
10:15 - 12:00
Ti 28.11.2017
12:15 - 14:00
Ma 4.12.2017
10:15 - 12:00
Ti 5.12.2017
12:15 - 14:00
Ma 11.12.2017
10:15 - 12:00
Ti 12.12.2017
12:15 - 14:00

### Muu opetus

06.09. - 18.10.2017 Ke 14.15-16.00
01.11. - 29.11.2017 Ke 14.15-16.00
07.12.2017 To 14.15-16.00
13.12.2017 Ke 14.15-16.00
Hans-Olav Tylli
Opetuskieli: englanti

### Materiaalit

The course will follow the course notes "Funktonaalianalyysin peruskurssi" (latest version 2012) by Kari Astala, Petteri Piiroinen & Hans-Olav Tylli. A current version for the Autumn 2017 will also be uploaded during the course (including notes indicating topics not covered this year during the lectures).

The following books contain related material (as well as much more), that can be used to compare with the course notes:

Bollobas: Linear Analysis (Cambridge Mathematical Textbooks)
Werner: Funktionalanalysis (Springer-Lehrbuch) [in German]
Rudin: Real and Complex Analysis (Tata McGraw-Hill) [chapters 3-5 used as material for this course]

## Muu

### Tehtävät

Improved hint for 1:4

### Kuvaus

Core course

Master's Programme in Mathematics and Statistics is responsible for the course.

Belongs to the Mathematics and Applied mathematics module.

The course is available to students from other degree programmes.

Analysis I&II, Linear algebra I&II, Topology I

Elements of measure theory and complex analysis

Elements of linear functional analysis including Banach and Hilbert spaces and linear operators between them, three basic principles, and applications to differential equations.

Recommended time/stage of studies for completion: 1. year

Term/teaching period when the course will be offered: varying

Introduction to linear functional analysis including Banach and Hilbert spaces and linear operators between them; topology of normed spaces; examples of Banach spaces including sequence and function spaces; three basic principles; Fourier-series; Sobolev spaces; applications to differential equations.

Required: