Mathematics

Ultrametric Calculus

An Introduction to P-Adic Analysis

Author: W. H. Schikhof

Publisher: Cambridge University Press

ISBN: 0521032873

Category: Mathematics

Page: 320

View: 2740

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.
Functional analysis

Advances in Ultrametric Analysis

Author: Alain Escassut,Cristina Perez-Garcia,Khodr Shamseddine

Publisher: American Mathematical Soc.

ISBN: 1470434911

Category: Functional analysis

Page: 290

View: 4939

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.
Mathematics

Advances in Ultrametric Analysis

12th International Conference on P-adic Functional Analysis, July 2-6, 2012, University of Manitoba, Winnipeg, Manitoba, Canada

Author: Khodr Shamseddine

Publisher: American Mathematical Soc.

ISBN: 0821891421

Category: Mathematics

Page: 291

View: 6531

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. The articles included in this book feature recent developments in various areas of non-archimedean analysis: branched values and zeros of the derivative of a $p$-adic meromorphic function, p-adic meromorphic functions $f^{\prime}P^{\prime}(f), g^{\prime}P^{\prime}(g)$ sharing a small function, properties of composition of analytic functions, partial fractional differentiability, morphisms between ultrametric Banach algebras of continuous functions and maximal ideals of finite dimension, the $p$-adic $q$-distributions, Banach spaces over fields with an infinite rank valuation, Grobman-Hartman theorems for diffeomorphisms of Banach spaces over valued fields, integral representations of continuous linear maps on $p$-adic spaces of continuous functions, non-Archimedean operator algebras, generalized Keller spaces over valued fields, proper multiplications on the completion of a totally ordered abelian group, the Grothendieck approximation theory in non-Archimedean functional analysis, generalized power series spaces, measure theory and the study of power series and analytic functions on the Levi-Civita fileds. 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.
Mathematics

An Introduction to Ultrametric Summability Theory

Author: Pinnangudi Natarajan

Publisher: Springer

ISBN: 8132225597

Category: Mathematics

Page: 159

View: 1888

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.
Mathematics

Ultrametric Functional Analysis

Eighth International Conference on P-adic Functional Analysis, July 5-9, 2004, Université Blaise Pascal, Clermont-Ferrand, France

Author: Bertin Diarra

Publisher: American Mathematical Soc.

ISBN: 0821836846

Category: Mathematics

Page: 369

View: 6095

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 (Clemont-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, functional analysis, and algebra.
Mathematics

Advances in Non-Archimedean Analysis

11th International Conference on P-Adic Functional Analysis, July 5-9 2010, Université Blaise Pascal, Clermont-Ferrand, France

Author: Jesus Araujo-Gomez,Bertin Diarra,Alain Escassut

Publisher: American Mathematical Soc.

ISBN: 0821852914

Category: Mathematics

Page: 280

View: 3588

This volume contains papers based on lectures given at the Eleventh International Conference on $p$-adic Functional Analysis, which was held from July 5-9, 2010, in Clermont-Ferrand, France. The articles collected here feature recent developments in various areas of non-Archimedean analysis: Hilbert and Banach spaces, finite dimensional spaces, topological vector spaces and operator theory, strict topologies, spaces of continuous functions and of strictly differentiable functions, isomorphisms between Banach function spaces, and measure and integration. Other topics discussed in this volume include $p$-adic differential and $q$-difference equations, rational and non-Archimedean analytic functions, the spectrum of some algebras of analytic functions, and maximal ideals of the ultrametric corona algebra.
Mathematics

Spinning Tops

A Course on Integrable Systems

Author: M. Audin

Publisher: Cambridge University Press

ISBN: 9780521779197

Category: Mathematics

Page: 148

View: 9754

Since the time of Lagrange and Euler, it has been well known that an understanding of algebraic curves can illuminate the picture of rigid bodies provided by classical mechanics. A modern view of the role played by algebraic geometry has been established iby many mathematicians. This book presents some of these techniques, which fall within the orbit of finite dimensional integrable systems. The main body of the text presents a rich assortment of methods and ideas from algebraic geometry prompted by classical mechanics, whilst in appendices the general, abstract theory is described. The methods are given a topological application to the study of Liouville tori and their bifurcations. The book is based on courses for graduate students given by the author at Strasbourg University but the wealth of original ideas will make it also appeal to researchers.
Mathematics

Ultrametric Functional Analysis

Eighth International Conference on P-adic Functional Analysis, July 5-9, 2004, Université Blaise Pascal, Clermont-Ferrand, France

Author: Bertin Diarra

Publisher: American Mathematical Soc.

ISBN: 9780821857175

Category: Mathematics

Page: 369

View: 9201

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.
Mathematics

Simon Stevin

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 7908

Mathematics

Report

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 3351

Mathematics

A Course in p-adic Analysis

Author: Alain M. Robert

Publisher: Springer Science & Business Media

ISBN: 1475732546

Category: Mathematics

Page: 438

View: 2289

Discovered at the turn of the 20th century, p-adic numbers are frequently used by mathematicians and physicists. This text is a self-contained presentation of basic p-adic analysis with a focus on analytic topics. It offers many features rarely treated in introductory p-adic texts such as topological models of p-adic spaces inside Euclidian space, a special case of Hazewinkel’s functional equation lemma, and a treatment of analytic elements.
Mathematics

L'Enseignement mathématique

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 2769

Vols. for 1965- include a separately paged section, Bulletin bibliographique.
Mathematics

Summability Calculus

A Comprehensive Theory of Fractional Finite Sums

Author: Ibrahim M. Alabdulmohsin

Publisher: Springer

ISBN: 3319746480

Category: Mathematics

Page: 165

View: 5926

This book develops the foundations of "summability calculus", which is a comprehensive theory of fractional finite sums. It fills an important gap in the literature by unifying and extending disparate historical results. It also presents new material that has not been published before. Importantly, it shows how the study of fractional finite sums benefits from and contributes to many areas of mathematics, such as divergent series, numerical integration, approximation theory, asymptotic methods, special functions, series acceleration, Fourier analysis, the calculus of finite differences, and information theory. As such, it appeals to a wide audience of mathematicians whose interests include the study of special functions, summability theory, analytic number theory, series and sequences, approximation theory, asymptotic expansions, or numerical methods. Richly illustrated, it features chapter summaries, and includes numerous examples and exercises. The content is mostly developed from scratch using only undergraduate mathematics, such as calculus and linear algebra.