MAT-62256 Advanced Functional Analysis, 7 cr


Suitable for postgraduate studies. Ei toteuteta lukuvuonna 2018-2019.


Lassi Paunonen, Esko Turunen


Toteutuskerta Periodi Vastuuhenkilö Suoritusvaatimukset
MAT-62256 2018-01 - Lassi Paunonen
Esko Turunen
Final exam


After completion of the course the student is mastering the foundations of the functional analysis the main results and is capable of deducing them from the definitions. The student can compute the generalized derivatives and apply them for solving partial differential equations. The student can explain different type of Sobolev spaces and knows their importance.


Sisältö Ydinsisältö Täydentävä tietämys Erityistietämys
1. Topological foundations Banach- ja Hilbert spaces Hahn-Banach theorem The open mapping theorem Baire category theorems Closed operator theorems   Weak topology.   
2. Generalized measure theory Rieszin representation theorem  The proofs involving results connecting Lebesgue and the generalized measure theory  The proof of the Riesz represention theorem 
3. Distribution theory and its applications to partial differential equations    The exact definition of tthe topology of the space of distributions  
4. Sobolev spaces     

Ohjeita opiskelijalle osaamisen tasojen saavuttamiseksi

The grade of the course is based on the final exam or two partial exams. When the points for the final exam or the partial exams are 30% of the maximum, the grade of the course may be improved by bonus points collected from the instructed exercises and homework. The passing limit is 50% of the maximum. If the student is mastering the concepts, results, short proofs and examples type of problems the evaluation is 3. For the grade 4 the student should in addition to the previous level be able to independently apply theory more. For the grade 5 the student should independently deduce results, invent solutions and compare results more than in the previous levels.


Numerical evaluation scale (0-5)


Completion parts must belong to the same implementation


Tyyppi Nimi Tekijä ISBN URL Lisätiedot Tenttimateriaali
Book   Functional Analysis   G. Bachman, L. Narici         No   
Book   Functional Analysis   Lax         No   
Book   Functional Analysis   Rudin         No   
Summary of lectures   MAT-53550 Advanced Functional Analysis   Eriksson         Yes   


Opintojakso P/S Selite
MAT-60206 Mathematical Analysis Advisable    
MAT-61006 Introduction to Functional Analysis Advisable    
MAT-61757 Measure and Integration Advisable    


Opintojakso Vastaa opintojaksoa  Selite 
MAT-62256 Advanced Functional Analysis, 7 cr MAT-53557 Advanced Functional Analysis, 8 cr  

Päivittäjä: Laaksonen Merja, 15.12.2018