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On the integral representation of finely superharmonic functions

Abderrahim Aslimani, Imad El Ghazi, Mohamed El Kadiri (2019)

Commentationes Mathematicae Universitatis Carolinae

In the present paper we study the integral representation of nonnegative finely superharmonic functions in a fine domain subset $U$ of a Brelot $𝒫$ -harmonic space $Ω$ with countable base of open subsets and satisfying the axiom $D$ . When $Ω$ satisfies the hypothesis of uniqueness, we define the Martin boundary of $U$ and the Martin kernel $K$ and we obtain the integral representation of invariant functions by using the kernel $K$ . As an application of the integral representation we extend to the cone $𝒮 (𝒰)$ of nonnegative...

On the mean value property of finely harmonic and finely hyperharmonic functions.

B. Fuglede (1990)

Aequationes mathematicae

On the sense preserving mappings in the Helm topology in the plane

Pyrih, Pavel (1999)

Serdica Mathematical Journal

∗Research supported by the grant No. GAUK 186/96 of Charles University.We introduce the helm topology in the plane. We show that (assuming the helm local injectivity and the Euclidean continuity) each mapping which is oriented at all points of a helm domain U is oriented at U.

Displaying 1 – 3 of 3

On the integral representation of finely superharmonic functions

On the mean value property of finely harmonic and finely hyperharmonic functions.

On the sense preserving mappings in the Helm topology in the plane

Currently displaying 1 – 3 of 3