Advances in Ultrametric Analysis

Alain Escassut · Cristina Perez-Garcia · Khodr Shamseddine

2018년 3월 · American Mathematical Soc.

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Articles included in this book feature recent developments in various areas of non-Archimedean analysis: summation of -adic series, rational maps on the projective line over , non-Archimedean Hahn-Banach theorems, ultrametric Calkin algebras, -modules with a convex base, non-compact Trace class operators and Schatten-class operators in -adic Hilbert spaces, algebras of strictly differentiable functions, inverse function theorem and mean value theorem in Levi-Civita fields, ultrametric spectra of commutative non-unital Banach rings, classes of non-Archimedean Köthe spaces, -adic Nevanlinna theory and applications, and sub-coordinate representation of -adic functions. Moreover, a paper on the history of -adic analysis with a comparative summary of non-Archimedean fields is presented.

Through a combination of new research articles and a survey paper, this book provides the reader with an overview of current developments and techniques in non-Archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.

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Edited by Alain Escassut: Université Clermont Auvergne, Aubiere, France,
Cristina Perez-Garcia: Universidad de Cantabria, Santander, Spain,
Khodr Shamseddine: University of Manitoba, Winnipeg, Canada