Analytic Elements In P-adic Analysis

ISBN: 9789810222345 出版年：1995 页码：403 Alain Escassut World Scientific Publishing Company

This is probably the first book dedicated to this topic. 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, factorization into meromorphic products and connections with Mittag-Leffler series. This is applied to the differential equation y'=hy (y,h analytic elements on D), analytic interpolation, injectivity, and to the p-adic Fourier transform.