Analytic Elements P Adic Analysis

The behaviour of the analytic elements on an infraconnected set D in K an algebraically closed complete ultrametric field is mainly explained by the circular filters and the monotonous filters on D, especially the T-filters: zeros of the elements, Mittag-Leffler series, factorization, Motzkin factorization, maximum principle, injectivity, algebraic properties of the algebra of the analytic elements on D, problems of analytic extension. This is applied to the differential equation y'=hy (y,h analytic elements on D), analytic interpolation, p-adic group duality on meromorphic products and to the p-adic Fourier transform.