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Let P=(P
t
)
t>0 be a submarkovian semigroup of kernels on a measurable space (X,). An additive kernel of P is a kernel K from X into ]0,[ such that P
t
K(x,A)=K(x,A+t) for every t>0,xX and every Borel subset A of ]0,[. It is proved in this paper that for every potential f of P, there exits an additive kernel K of P, unique (up to equivalence) such that f=K1=0
K(,dt). This result is already well known for regular potentials of right processes. If U=(U
p
)
p>0 is a sub-Markovian resolvent of kernels on (X,), we give a notion of additive kernel of U and we prove a similar integral representation of potentials of U. 相似文献
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Mohamed Hmissi 《manuscripta mathematica》1992,75(1):293-302
Let ℙ=(P
t
)
t<0
be a semigroup of kernel and letm be an excessive reference measure for ℙ. In this work we prove that ℙ ism-basic if and only if everym.a.e. finite purely excessive function is represented by a unique exit law for ℙ. In this case we deduce some applications
about natural densities, energie functionnal and invariant functions for the time-space semigroup of ℙ.
相似文献
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Mohamed Hmissi 《Potential Analysis》1994,3(1):145-152
Let (X, ) be a continuous dynamical system on a locally compact spaceX with countable base. In this note we prove the equivalence of the following statements:
As application, every unstable dynamical system possesses a sectionS in the formS={p=q}, such thatp andq are lower semicontinuous and >0 onX. 相似文献
1. | (X, ) is unstable; |
2. | The kernelf Vf= 0 f((t, ·)) dt, is a proper kernel. |
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