This volume contains research articles based on lectures given at the Seventh International Conference on $p$-adic Functional Analysis. The articles, written by leading international experts, provide a complete overview of the latest contributions in basic functional analysis (Hilbert and Banach spaces, locally convex spaces, orthogonality, inductive limits, spaces of continuous functions, strict topologies, operator theory, automatic continuity, measure and integrations, Banach and topological algebras, summability methods, and ultrametric spaces), analytic functions (meromorphic functions, roots of rational functions, characterization of injective holomorphic functions, and Gelfand transforms in algebras of analytic functions), differential equations, Banach-Hopf algebras, Cauchy theory of Levi-Civita fields, finite differences, weighted means, $p$-adic dynamical systems, and non-Archimedean probability theory and stochastic processes. The book is written for graduate students and research mathematicians. It also would make a good reference source for those in related areas, such as classical functional analysis, complex analytic functions, probability theory, dynamical systems, orthomodular spaces, number theory, and representations of $p$-adic groups.

With contributions by leading mathematicians, this proceedings volume reflects the program of the Eighth International Conference on $p$-adic Functional Analysis held at Blaise Pascal University (Clermont-Ferrand, France). Articles in the book offer a comprehensive overview of research in the area. A wide range of topics are covered, including basic ultrametric functional analysis, topological vector spaces, measure and integration, Choquet theory, Banach and topological algebras,analytic functions (in particular, in connection with algebraic geometry), roots of rational functions and Frobenius structure in $p$-adic differential equations, and $q$-ultrametric calculus. The material is suitable for graduate students and researchers interested in number theory, functionalanalysis, and algebra.

This is an introduction to p-adic analysis which is elementary yet complete and which displays the variety of applications of the subject. Dr Schikhof is able to point out and explain how p-adic and 'real' analysis differ. This approach guarantees the reader quickly becomes acquainted with this equally 'real' analysis and appreciates its relevance. The reader's understanding is enhanced and deepened by the large number of exercises included throughout; these both test the reader's grasp and extend the text in interesting directions. As a consequence, this book will become a standard reference for professionals (especially in p-adic analysis, number theory and algebraic geometry) and will be welcomed as a textbook for advanced students of mathematics familiar with algebra and analysis.

This is the second, completely revised and expanded edition of the author’s first book, covering numerous new topics and recent developments in ultrametric summability theory. Ultrametric analysis has emerged as an important branch of mathematics in recent years. This book presents a brief survey of the research to date in ultrametric summability theory, which is a fusion of a classical branch of mathematics (summability theory) with a modern branch of analysis (ultrametric analysis). Several mathematicians have contributed to summability theory as well as functional analysis. The book will appeal to both young researchers and more experienced mathematicians who are looking to explore new areas in analysis. The book is also useful as a text for those who wish to specialize in ultrametric summability theory.

This volume contains papers based on lectures given at the 12th International Conference on p-adic Functional Analysis, which was held at the University of Manitoba on July 2-6, 2012. Through a combination of new research articles and survey papers, 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.

"Contains research articles by nearly 40 leading mathematicians from North and South America, Europe, Africa, and Asia, presented at the Fourth International Conference on p-adic Functional Analysis held recently in Nijmegen, The Netherlands. Includes numerous new open problems documented with extensive comments and references."

This volume collects together lectures presented at the Sixth International Conference held at the University of Ioannina, Greece, on p-adic functional analysis with applications in the fields of physics, differential equations, number theory, probability theory, dynamical systems, and algebraic number fields. It discusses the commutation relation AB-BA=I and its central role in quantum mechanics.