Décomposition en éléments simples d'une fonction analytique sur un corps ultramétrique. Application au prolongement analytique
We discuss a new formulation of the linear theory of discrete complex analysis on planar quad-graphs based on their medial graphs. It generalizes the theory on rhombic quad-graphs developed by Duffin, Mercat, Kenyon, Chelkak and Smirnov and follows the approach on general quad-graphs proposed by Mercat. We provide discrete counterparts of the most fundamental objects in complex analysis such as holomorphic functions, differential forms, derivatives, and the Laplacian. Also, we discuss discrete versions...
It is shown that a finite system T of matrices whose real linear combinations have real spectrum satisfies a bound of the form . The proof appeals to the monogenic functional calculus.