Advances in Ultrametric Analysis (eBook)

This book contains the proceedings of the 14th International Conference on $p$-adic Functional Analysis, held from June 30-July 4, 2016, at the Universite d'Auvergne, Aurillac, France. Articles included in this book feature recent developments in various areas of non-Archimedean analysis: summation of $p$-adic series, rational maps on the projective line over $/mathbb{Q}p$, non-Archimedean Hahn-Banach theorems, ultrametric Calkin algebras, $G$-modules with a convex base, non-compact Trace class operators and Schatten-class operators in $p$-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 Koethe spaces, $p$-adic Nevanlinna theory and applications, and sub-coordinate representation of $p$-adic functions. Moreover, a paper on the history of $p$-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.