Valeurs aux entiers négatifs des fonctions et fonctions -adiques d’un corps de nombres totalement réel
In this paper, we establish an one-to-one mapping between complex-valued functions defined on and complex-valued functions defined on -adic number field , and introduce the definition and method of Weyl-Heisenberg frame on hormonic analysis to -adic anylysis.
We prove an inequality linking the growth of a generalized Wronskian of m p-adic power series to the growth of the ordinary Wronskian of these m power series. A consequence is that if the Wronskian of m entire p-adic functions is a non-zero polynomial, then all these functions are polynomials. As an application, we prove that if a linear differential equation with coefficients in ℂₚ[x] has a complete system of solutions meromorphic in all ℂₚ, then all the solutions of the differential equation are...