A Singular Convolution Equation In The Space Of Distributions II

Dragiša Mitrović

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A Singular Convolution Equation In The Space Of Distributions

Dragiša Mitrović (1977)

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This second part of our two part work on i.d. process has four main goals: (1) To develop a potential operator for recurrent i.d. (infinitely divisible) processes and to use this operator to find the asymptotic behavior of the hitting distribution and Green’s function for relatively compact sets in the recurrent case. (2) To develop the appropriate notion of an equilibrium measure and Robin’s constant for Borel sets. (3) To establish the asymptotic...

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C. A. Berenstein, M. A. Dostal (1973)

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Using a description of the topology of the spaces $E^{'} (Ω)$ ( $Ω$ open convex subset of $R^{n}$ ) via the Fourier transform, namely their analytically uniform structures, we arrive at a formula describing the convex hull of the singular support of a distribution $T$ , $T \in E^{'}$ . We give applications to a class of distributions $T$ satisfying $cv. sing. supp. S * T = cv. sing. supp. S + cv. sing. supp. T$ for all $S \in E^{'}$ .