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
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.
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
Affiliations des auteurs :
Tomasz Klimsiak 1 ; Andrzej Rozkosz 1
@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/}
}
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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
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