La formule du caractère et la formule de Plancherel pour les groupes de Lie résolubles presque connexes sur un corps p-adique

Following Duflo–Vergne (for real reductive groups) and Khalgui–Torasso (for real almost algebraic groups), we prove a Plancherel formula for almost connected solvable p-adic groups (p≠2). To do this, we give a necessary and sufficient condition for a unitary irreducible representation to be admissible in terms of Kirillov–Duflo orbit method. Then we establish a character formula around each semi-simple element.