Geodesic
On the structure of bounded smooth measures associated with a quasi-regular Dirichlet form
Tomasz Klimsiak1 ; Andrzej Rozkosz1
1 Faculty of Mathematics and Computer Science Nicolaus Copernicus University 87-100 Toruń, Poland
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 65 (2017) no. 1, pp. 45-56.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We consider a quasi-regular Dirichlet form. We show that a bounded signed measure charges no set of zero capacity associated with the form if and only if the measure can be decomposed into the sum of an integrable function and a bounded linear functional on the domain of the form. The decomposition allows one to describe explicitly the set of bounded measures charging no sets of zero capacity for interesting classes of Dirichlet forms. By way of illustration, some examples are given.
DOI : 10.4064/ba8108-7-2017
Keywords: consider quasi regular dirichlet form bounded signed measure charges set zero capacity associated form only measure decomposed sum integrable function bounded linear functional domain form decomposition allows describe explicitly set bounded measures charging sets zero capacity interesting classes dirichlet forms illustration examples given

Tomasz Klimsiak 1 ; Andrzej Rozkosz 1

1 Faculty of Mathematics and Computer Science Nicolaus Copernicus University 87-100 Toruń, Poland 
@article{10_4064_ba8108_7_2017,
     author = {Tomasz Klimsiak and Andrzej Rozkosz},
     title = {On the structure of bounded smooth measures associated with a quasi-regular {Dirichlet} form},
     journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
     pages = {45--56},
     publisher = {mathdoc},
     volume = {65},
     number = {1},
     year = {2017},
     doi = {10.4064/ba8108-7-2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ba8108-7-2017/}
}
TY  - JOUR
AU  - Tomasz Klimsiak
AU  - Andrzej Rozkosz
TI  - On the structure of bounded smooth measures associated with a quasi-regular Dirichlet form
JO  - Bulletin of the Polish Academy of Sciences. Mathematics
PY  - 2017
SP  - 45
EP  - 56
VL  - 65
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ba8108-7-2017/
DO  - 10.4064/ba8108-7-2017
LA  - en
ID  - 10_4064_ba8108_7_2017
ER  - 
%0 Journal Article
%A Tomasz Klimsiak
%A Andrzej Rozkosz
%T On the structure of bounded smooth measures associated with a quasi-regular Dirichlet form
%J Bulletin of the Polish Academy of Sciences. Mathematics
%D 2017
%P 45-56
%V 65
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/ba8108-7-2017/
%R 10.4064/ba8108-7-2017
%G en
%F 10_4064_ba8108_7_2017
Tomasz Klimsiak; Andrzej Rozkosz. On the structure of bounded smooth measures associated with a quasi-regular Dirichlet form. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 65 (2017) no. 1, pp. 45-56. doi : 10.4064/ba8108-7-2017. http://geodesic.mathdoc.fr/articles/10.4064/ba8108-7-2017/

Cité par Sources :