We define the Laplacian on an arbitrary set with a not necessarily symmetric weight function and discuss the Dirichlet problem and other classical topics in this setting.

We study the singularities of plurisubharmonic functions using methods from convexity theory. Analyticity theorems for a refined Lelong number are proved.

We characterize straightness of digital curves in the integer plane by means of difference operators. Earlier definitions of digital rectilinear segments have used, respectively, Rosenfeldâ€™s chordâ€¦ (More)

Tangents of plurisubharmonic functions Local properties of plurisubharmonic functions are studied by means of the notion of tangent which describes the behavior of the function near a given point. Weâ€¦ (More)

We study discrete analogues of holomorphic functions of one and two variables, especially those that were called monodiffric functions of the first kind by Rufus Isaacs. Discrete analogues of theâ€¦ (More)

The theme of these lectures is local and global properties of plurisubharmonic functions. First differential inequalities defining convex, subharmonic and plurisubharmonic functions are discussed. Itâ€¦ (More)

A distance transformation gives for every set in the image plane a function which measures the distance to the set. Several different methods of measuring the distance are possible, and some haveâ€¦ (More)

Efim Khalimskyâ€™s digital Jordan curve theorem states that the complement of a Jordan curve in the digital plane equipped with the Khalimsky topology has exactly two connectivity components. Weâ€¦ (More)