Displaying similar documents to “On Deny's characterization of the potential kernel for a convolution Feller semi-group”

The convolution equation of Choquet and Deny and relatively invariant measures on semigroups

Arunava Mukherjea (1971)

Annales de l'institut Fourier

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Choquet and Deny considered on an abelian locally compact topological group the representation of a measure as the convolution product of itself and a finite measure . In this paper, we make an attempt to find, in the case of certain locally compact semigroups, those solutions of the above equation which are relatively invariant on the support of . A characterization of relatively invariant measures on certain locally compact semigroups is also presented. Our results...

On the Green type kernels on the half space in

Masayuki Itô (1978)

Annales de l'institut Fourier

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We characterize the Hunt convolution kernels on () whose the Green type kernels on ; , , satisfy the domination principle. We write and the restriction of to . This gives that the question raised by H.L. Jackson is affirmatively solved.

Some remarks on the existence of a resolvent

Masanori Kishi (1975)

Annales de l'institut Fourier

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Noting that a resolvent is associated with a convolution kernel satisfying the domination principle if and only if has the dominated convergence property, we give some remarks on the existence of a resolvent.

A new setting for potential theory. I

Kai Lai Chung, K. Murali Rao (1980)

Annales de l'institut Fourier

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We consider a transient Hunt process in which the potential density satisfies the conditions: (a) for each , is finite continuous in ; (b) iff . In earlier papers Chung established an equilibrium principle, and Rao obtained a Riesz of decomposition for excessive functions. We now begin a deeper study under these conditions, including the uniqueness of the decomposition and Hunt’s hypothesis (B).