Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-71-11-K-7

Introduction to the Theory of Dirichlet Forms (4V+2U, 9.0 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 9.0 CP 186 h
4 V Lecture 56 h
2 U Exercise class (in small groups) 28 h
(4V+2U) 9.0 CP 84 h 186 h

Basedata

SWS 4V+2U
CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. irreg.
Level [7] Master (Advanced)
Language [EN] English
Lecturers
+ further Lecturers of the department Mathematics
Area of study [MAT-SPAS] Analysis and Stochastics
Additional informations
Livecycle-State [NORM] Active

Contents

  • 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).

Literature

  • 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.

Materials

Further literature will be announced in the lecture; Exercise material is provided.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

Requirements for attendance (informal)

Modules:

Requirements for attendance (formal)

None

References to Course [MAT-71-11-K-7]

Module Name Context
[MAT-71-11-M-7] Introduction to the Theory of Dirichlet Forms P: Obligatory 4V+2U, 9.0 LP