- resolvents, semigroups, generators (Theorem of Hille and Yosida),
- coercive bilinear forms (Stampacchia theorem, characterisation by resolvents, semigroups, generators),
- closed bilinear form,
- contraction properties (Sub-Markov property, Dirichlet operators, Dirichlet forms).
Introduction to the Theory of Dirichlet Forms (M, 9.0 LP)
|Module Number||Module Name||CP (Effort)|
|MAT-71-11-M-7||Introduction to the Theory of Dirichlet Forms||9.0 CP (270 h)|
|CP, Effort||9.0 CP = 270 h|
|Position of the semester||1 Sem. irreg.|
|Level|| Master (Advanced)|
+ further Lecturers of the department Mathematics
|Area of study||[MAT-SPAS] Analysis and Stochastics|
|Reference course of study||[MAT-88.105-SG] M.Sc. Mathematics|
|Type/SWS||Course Number||Title||Choice in |
|SL||SL is |
required for exa.
Introduction to the Theory of Dirichlet Forms
|P||84 h||186 h||-||-||PL1||9.0||irreg.|
- About [MAT-71-11-K-7]: Title: "Introduction to the Theory of Dirichlet Forms"; Presence-Time: 84 h; Self-Study: 186 h
Examination achievement PL1
- Form of examination: oral examination (20-30 Min.)
- Examination Frequency: each semester
- Examination number: 86255 ("Introduction to the Theory of Dirichlet Forms")
Evaluation of grades
The grade of the module examination is also the module grade.
Competencies / intended learning achievements
By solving the given exercise problems, they have gained a precise and independent handling of the terms, propositions and methods of the lecture. In addition, they have learned to apply the methods to new problems, analyze them and develop solution strategies independently or by team work.
- Z.-M. Ma, M. Röckner: Introduction to the theory of (non-symmetric) Dirichlet forms,
- M. Fukushima: Dirichlet Forms and Markov Processes,
- M. Reed, B. Simon: Methods of modern mathematical physics I.
Requirements for attendance (informal)
- [MAT-10-1-M-2] Fundamentals of Mathematics (M, 28.0 LP)
- [MAT-70-11-M-4] Functional Analysis (M, 9.0 LP)