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

The convolution equation P = P * Q 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 P as the convolution product of itself and a finite measure Q : P = P * Q . In this paper, we make an attempt to find, in the case of certain locally compact semigroups, those solutions P of the above equation which are relatively invariant on the support of Q . 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 ℝ n

Masayuki Itô (1978)

Annales de l'institut Fourier

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We characterize the Hunt convolution kernels χ on R n ( n ≥ 2 ) whose the Green type kernels on D = { ( x 1 , ... , x n ) ∈ R n ; x 1 > 0 } , V χ : C K ( D ) ∋ f ( χ * f - χ * χ ‾ ) D , satisfy the domination principle. We write f ‾ ( x 1 , x 2 , ... , x n ) = f ( - x 1 , x 2 , ... , x n ) and ( · ) D the restriction of ( · ) to D . 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 x satisfying the domination principle if and only if x 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 u satisfies the conditions: (a) for each x , u ( x , y ) - 1 is finite continuous in y ; (b) u ( x , y ) = + ∞ iff x = y . 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).