Ultrametric Functional Analysis
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Author |
: Wilhelmus Hendricus Schikhof |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 434 |
Release |
: 2003 |
ISBN-10 |
: 9780821833209 |
ISBN-13 |
: 0821833200 |
Rating |
: 4/5 (09 Downloads) |
Synopsis Ultrametric Functional Analysis by : Wilhelmus Hendricus Schikhof
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.
Author |
: Bertin Diarra |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 384 |
Release |
: 2005 |
ISBN-10 |
: 9780821836842 |
ISBN-13 |
: 0821836846 |
Rating |
: 4/5 (42 Downloads) |
Synopsis Ultrametric Functional Analysis by : Bertin Diarra
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.
Author |
: Khodr Shamseddine |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 305 |
Release |
: 2013 |
ISBN-10 |
: 9780821891421 |
ISBN-13 |
: 0821891421 |
Rating |
: 4/5 (21 Downloads) |
Synopsis Advances in Ultrametric Analysis by : Khodr Shamseddine
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.
Author |
: Alain Escassut |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 298 |
Release |
: 2018-03-26 |
ISBN-10 |
: 9781470434915 |
ISBN-13 |
: 1470434911 |
Rating |
: 4/5 (15 Downloads) |
Synopsis Advances in Ultrametric Analysis by : Alain Escassut
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.
Author |
: W. H. Schikhof |
Publisher |
: Cambridge University Press |
Total Pages |
: 0 |
Release |
: 2007-01-25 |
ISBN-10 |
: 9780521032872 |
ISBN-13 |
: 0521032873 |
Rating |
: 4/5 (72 Downloads) |
Synopsis Ultrametric Calculus by : W. H. Schikhof
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.
Author |
: P.N. Natarajan |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 111 |
Release |
: 2013-10-18 |
ISBN-10 |
: 9788132216476 |
ISBN-13 |
: 8132216474 |
Rating |
: 4/5 (76 Downloads) |
Synopsis An Introduction to Ultrametric Summability Theory by : P.N. Natarajan
Ultrametric analysis has emerged as an important branch of mathematics in recent years. This book presents, for the first time, 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.
Author |
: Alain Escassut |
Publisher |
: |
Total Pages |
: 298 |
Release |
: 2018 |
ISBN-10 |
: 1470446766 |
ISBN-13 |
: 9781470446765 |
Rating |
: 4/5 (66 Downloads) |
Synopsis Advances in Ultrametric Analysis by : Alain Escassut
On non-Archimedean valued fields / Angel Barría Comicheo and Khodr Shamseddine -- http://www.ams.org/conm/704/ https://doi.org/10.1090/conm/704/14158 Non-compact Trace class operators and Schatten-class operators in $p$-adic Hilbert spaces / S. Basu -- http://www.ams.org/conm/704/ https://doi.org/10.1090/conm/704/14159 Calculus on a non-Archimedean field extension of the real numbers: inverse function theorem, intermediate value theorem and mean value theorem / Gidon Bookatz and Khodr Shamseddine -- http://www.ams.org/conm/704/ https://doi.org/10.1090/conm/704/14160 $p$-adic meromorphic functions $f'P'(f), g'P'(g)$ sharing a small function, ignoring multiplicity / Kamal Boussaf and Alain Escassut -- http://www.ams.org/conm/704/ https://doi.org/10.1090/conm/704/14161 Spectra of commutative non-unital Banach rings / Chi-Wai Leung and Chi-Keung Ng -- http://www.ams.org/conm/704/ https://doi.org/10.1090/conm/704/14162 Ultrametric Calkin algebras / Bertin Diarra -- http://www.ams.org/conm/704/ https://doi.org/10.1090/conm/704/14163 On summation of $p$-adic series / Branko Dragovich -- http://www.ams.org/conm/704/ https://doi.org/10.1090/conm/704/14164 Spectrum of ultrametric Banach algebras of strictly differentiable functions / Alain Escassut and Nicolas Maïnetti -- http://www.ams.org/conm/704/ https://doi.org/10.1090/conm/704/14165 Classical $p$-adic Nevanlinna theory and Nevalinna Theory out of a hole / Alain Escassut and Ta Thi Hoai An -- http://www.ams.org/conm/704/ https://doi.org/10.1090/conm/704/14166 The distance preserving mappings and isometrics defined on non-Archimedean Banach spaces / Albert Kubzdela -- http://www.ams.org/conm/704/ https://doi.org/10.1090/conm/704/14167 Rational map $ax+1/x$ on the projective line over $\mathbb {Q}_{p}$ / Shilei Fan and Lingmin Liao -- http://www.ams.org/conm/704/ https://doi.org/10.1090/conm/704/14168 Non-Archimedean Hahn-Banach theorems and injective Banach spaces / M. González and C. Perez-Garcia -- http://www.ams.org/conm/704/ https://doi.org/10.1090/conm/704/14169 $G$-modules with a convex base / H. Ochsenius and E. Olivos -- http://www.ams.org/conm/704/ https://doi.org/10.1090/conm/704/14170 A journey throughout the history of $p$-adic numbers / Yvette Perrin -- http://www.ams.org/conm/704/ https://doi.org/10.1090/conm/704/14171 On some classes of non-Archimedean Köthe spaces / Wiesław Śliwa and Agnieszka Ziemkowska -- http://www.ams.org/conm/704/ https://doi.org/10.1090/conm/704/14172 On the sub-coordinate representation of $p$-adic functions / Ekaterina Yurova Axelsson -- http://www.ams.org/conm/704/ https://doi.org/10.1090/conm/704/14173
Author |
: P.N. Natarajan |
Publisher |
: Springer |
Total Pages |
: 169 |
Release |
: 2015-09-08 |
ISBN-10 |
: 9788132225591 |
ISBN-13 |
: 8132225597 |
Rating |
: 4/5 (91 Downloads) |
Synopsis An Introduction to Ultrametric Summability Theory by : P.N. Natarajan
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.
Author |
: Arnoud C. M. Rooij |
Publisher |
: |
Total Pages |
: 432 |
Release |
: 1978 |
ISBN-10 |
: UCAL:B4405261 |
ISBN-13 |
: |
Rating |
: 4/5 (61 Downloads) |
Synopsis Non-Archimedean Functional Analysis by : Arnoud C. M. Rooij
Author |
: Peter Schneider |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 159 |
Release |
: 2013-03-09 |
ISBN-10 |
: 9783662047286 |
ISBN-13 |
: 3662047284 |
Rating |
: 4/5 (86 Downloads) |
Synopsis Nonarchimedean Functional Analysis by : Peter Schneider
This book grew out of a course which I gave during the winter term 1997/98 at the Universitat Munster. The course covered the material which here is presented in the first three chapters. The fourth more advanced chapter was added to give the reader a rather complete tour through all the important aspects of the theory of locally convex vector spaces over nonarchimedean fields. There is one serious restriction, though, which seemed inevitable to me in the interest of a clear presentation. In its deeper aspects the theory depends very much on the field being spherically complete or not. To give a drastic example, if the field is not spherically complete then there exist nonzero locally convex vector spaces which do not have a single nonzero continuous linear form. Although much progress has been made to overcome this problem a really nice and complete theory which to a large extent is analogous to classical functional analysis can only exist over spherically complete field8. I therefore allowed myself to restrict to this case whenever a conceptual clarity resulted. Although I hope that thi8 text will also be useful to the experts as a reference my own motivation for giving that course and writing this book was different. I had the reader in mind who wants to use locally convex vector spaces in the applications and needs a text to quickly gra8p this theory.