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On a Singular Value Problem for the Fractional Laplacian on the Exterior of the Unit Ball

Bezzarga, Mounir; Kefi, Khaled — 2005

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: Primary 26A33; Secondary 47G20, 31B05 We study a singular value problem and the boundary Harnack principle for the fractional Laplacian on the exterior of the unit ball.

Regular potentials of additive functionals in semidynamical systems

Nedra Belhaj Rhouma; Mounir Bezzarga — 2004

Commentationes Mathematicae Universitatis Carolinae

We consider a semidynamical system $(X, ℬ, Φ, w)$ . We introduce the cone $𝔸$ of continuous additive functionals defined on $X$ and the cone $𝒫$ of regular potentials. We define an order relation “ $\leq$ ” on $𝔸$ and a specific order “ $≺$ ” on $𝒫$ . We will investigate the properties of $𝔸$ and $𝒫$ and we will establish the relationship between the two cones.

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