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On exit laws for semigroups in weak duality

Imed Bachar — 2001

Commentationes Mathematicae Universitatis Carolinae

Let $ℙ : = {(P_{t})}_{t > 0}$ be a measurable semigroup and $m$ a $σ$ -finite positive measure on a Lusin space $X$ . An $m$ -exit law for $ℙ$ is a family ${(f_{t})}_{t > 0}$ of nonnegative measurable functions on $X$ which are finite $m$ -a.e. and satisfy for each $s, t > 0$ $P_{s} f_{t} = f_{s + t}$ $m$ -a.e. An excessive function $u$ is said to be in $ℛ$ if there exits an $m$ -exit law ${(f_{t})}_{t > 0}$ for $ℙ$ such that $u = \int_{0}^{\infty} f_{t} d t$ , $m$ -a.e. Let $𝒫$ be the cone of $m$ -purely excessive functions with respect to $ℙ$ and $ℐ m V$ be the cone of $m$ -potential functions. It is clear that $ℐ m V \subseteq ℛ \subseteq 𝒫$ . In this paper we are...

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Currently displaying 1 – 8 of 8

On exit laws for semigroups in weak duality

Estimates for the Green function and existence of positive solutions for higher-order elliptic equations.

Existence of positive solutions for higher order singular sublinear elliptic equations.

Estimates for the Green function and characterization of a certain Kato class by the Gauss semigroup in the half space.

On some quasimetrics and their applications.

Existence of positive solutions to nonlinear elliptic problem in the half space.

Positive solutions of nonlinear elliptic equations in a half space in $ℝ^{2}$ .

Estimates for the Green function and singular solutions for polyharmonic nonlinear equation.