Choquet Theory, Boundaries and Applications II - NRFA044

• Title: Choquetova teorie, hranice a aplikace II
• Guaranteed by: Department of Mathematical Analysis (32-KMA)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2013 to 2018
• Semester: summer
• E-Credits: 3
• Hours per week, examination: summer s.:2/0, Ex [HT]
• Capacity: unlimited
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: not taught
• Language: Czech
• Teaching methods: full-time
• Teaching methods: full-time
• Class: DS, matematická analýza
• Classification: Mathematics > Functional Analysis
• Is incompatible with: NMMA474

Annotation

English

Last update: T_KMA (18.05.2010)

This course is a continuation of lectures on Choquet's theory.

Czech

Last update: T_KMA (06.05.2010)

V přednášce, která je volným pokračováním přednášky NRFA008, budou ukázány různé aplikace vět o integrální reprezentaci.

Syllabus

English

Last update: T_KMA (04.05.2006)

Integral representation of positive harmonic functions by minimal

harmonic functions, Martin boundary. Simpliciality of the space of continuous

functions on a compact set which are harmonic on a dense open subset (on an open neighborhood respectively). ,

Dichotomy of the lattice structure for the classical case

(in contrast to the heat equation case),

Determination of the Choquet boundaries, probabilistic

characterization, minimal representing measures, description of

all representing measures and corresponding concave functions.

Representing measures (minimal) with respect to the cone of potentials.

Czech

Last update: T_KMA (24.01.2007)

Integrální reprezentace pozitivních harmonických funkcí pomocí minimálních, Martinova hranice. Simplicialita prostorů funkcí a Choquetova hranice v teorii potenciálu. Svazová dichotomie klasické i tepelné teorie. Pravděpodobnostní interpretace. Reprezentující míry kuželů potenciálů.

E. M. Alfsen, Compact convex sets and boundary integrals, 1971,

G. Choquet, Lectures on analysis II, 1969,

R. R. Phelps, Lectures on Choquet's theorem, 2001,

E. G. Effros and J. L. Kazdan, Applications of Choquet simplexes to elliptic and parabolic boundary value problems, J. Diff. Eq. 8(1970), 95-134