| Title:
|
On the integral representation of finely superharmonic functions (English) |
| Author:
|
Aslimani, Abderrahim |
| Author:
|
El Ghazi, Imad |
| Author:
|
El Kadiri, Mohamed |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
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60 |
| Issue:
|
3 |
| Year:
|
2019 |
| Pages:
|
323-350 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present paper we study the integral representation of nonnegative finely superharmonic functions in a fine domain subset $U$ of a Brelot $\mathcal{P}$-harmonic space $\Omega$ with countable base of open subsets and satisfying the axiom $D$. When $\Omega$ satisfies the hypothesis of uniqueness, we define the Martin boundary of $U$ and the Martin kernel $K$ and we obtain the integral representation of invariant functions by using the kernel $K$. As an application of the integral representation we extend to the cone $\mathcal{S(U)}$ of nonnegative finely superharmonic functions in $U$ a partition theorem of Brelot. We also establish an approximation result of invariant functions by finely harmonic functions in the case where the minimal invariant functions are finely harmonic. (English) |
| Keyword:
|
finely harmonic function |
| Keyword:
|
finely superharmonic function |
| Keyword:
|
fine potential |
| Keyword:
|
fine Green kernel |
| Keyword:
|
integral representation |
| Keyword:
|
Martin boundary |
| Keyword:
|
fine Riesz-Martin kernel |
| MSC:
|
31C35 |
| MSC:
|
31C40 |
| MSC:
|
31D05 |
| idZBL:
|
Zbl 07144898 |
| idMR:
|
MR4034436 |
| DOI:
|
10.14712/1213-7243.2019.019 |
| . |
| Date available:
|
2019-10-29T12:56:32Z |
| Last updated:
|
2021-10-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147852 |
| . |
| Reference:
|
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