Displaying similar documents to “On spaces of potentials connected with L p classes”

Infinitely divisible processes and their potential theory. I

Sidney C. Port, Charles J. Stone (1971)

Annales de l'institut Fourier

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We show that associated with every i.d. (infinitely divisible) process on a locally compact, non-compact 2nd countable Abelian group is a corresponding potential theory that yields definitive results on the behavior of the process in both space and time. Our results are general, no density or other smoothness assumptions are made on the process. In this first part of two part work we have four main goals. (1) To lay the probabilistic foundation of such processes. This mainly...

Theory of Bessel potentials. II

Robert Adams, Nachman Aronszajn, K. T. Smith (1967)

Annales de l'institut Fourier

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Dans cette partie de la théorie des potentiels besseliens on considère les restrictions de potentiels de la classe P a ( R n ) aux domaines ouverts D R n . On cherche à caractériser de manière intrinsèque la classe P a ( D ) ainsi obtenue. On attaque ce problème en définissant de manière directe (§ 2) une classe P ˇ a ( D ) P a ( D ) qui, pour des domaines assez réguliers, est égale à P a ( D ) . L’égalité P a ( D ) = P a ( D ) est équivalente à l’existence d’un opérateur-extension E : P ˇ a ( D ) P a ( R n ) , linéaire et continu, tel que E u soit une extension...

Infinitely divisible processes and their potential theory. II

Sidney C. Port, Charles J. Stone (1971)

Annales de l'institut Fourier

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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...