| Title:
|
On exit laws for semigroups in weak duality (English) |
| Author:
|
Bachar, Imed |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
4 |
| Year:
|
2001 |
| Pages:
|
711-719 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $\Bbb P:=(P_{t})_{t>0}$ be a measurable semigroup and $m$ a $\sigma $-finite positive measure on a Lusin space $X$. An $m$-exit law for $\Bbb P$ is a family $(f_{t})_{t>0}$ of nonnegative measurable functions on $X$ which are finite $m$-a.e. and satisfy for each $s,t >0$ $P_{s}f_{t}=f_{s+t}$ $m$-a.e. An excessive function $u$ is said to be in $\Cal R$ if there exits an $m$-exit law $(f_{t})_{t>0}$ for $\Bbb P$ such that $u=\int_{0}^{\infty }f_{t}\,dt$, $m$-a.e. Let $\Cal P$ be the cone of $m$-purely excessive functions with respect to $\Bbb P$ and $\Cal I mV$ be the cone of $m$-potential functions. It is clear that $\Cal I mV\subseteq \Cal R\subseteq \Cal P$. In this paper we are interested in the converse inclusion. We extend some results already obtained under the assumption of the existence of a reference measure. Also, we give an integral representation of the mutual energy function. (English) |
| Keyword:
|
semigroup |
| Keyword:
|
weak duality |
| Keyword:
|
exit law |
| MSC:
|
31D05 |
| MSC:
|
60J45 |
| idZBL:
|
Zbl 1090.31501 |
| idMR:
|
MR1883379 |
| . |
| Date available:
|
2009-01-08T19:18:00Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119286 |
| . |
| Reference:
|
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| . |
