Overview

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.Contents: Absolute Values and NormsInfraconnected SetsMonotonous and Circular FiltersUltrametric Absolute Values and Valuation Functions (h, ) on K (x) Hensel LemmaThe Analytic ElementsFactorization of Analytic ElementsThe Mittage Leffler TheoremDerivative of Analytic ElementsElements Vanishing Along a FilterQuasi-Minorated ElementsAnalytic Elements Meromorphic in a HoleMotzkin FactorizationMaximum in a Circle with Holes T -Filters and T -SequencesIntegrally Closed Algebras H (D) Absolute Values in Algebras H (D) Idempotent T- SequencesAlgebra H(D) / I0(F) Injectivity, Mittag Leffler Series and Motzkin ProductsGeneralities on the Differential Equation y' = fy in H (D) The Equation y' = fy in Zero Residue Characteristicand other papersReadership: Mathematicians.

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9781299635753

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