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Author: Bertin Diarra Publisher: American Mathematical Soc. ISBN: 0821836846 Category : Topological fields Languages : en Pages : 384
Book Description
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: Bertin Diarra Publisher: American Mathematical Soc. ISBN: 0821836846 Category : Topological fields Languages : en Pages : 384
Book Description
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: Wilhelmus Hendricus Schikhof Publisher: American Mathematical Soc. ISBN: 0821833200 Category : p-adic analysis Languages : en Pages : 434
Book Description
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: Khodr Shamseddine Publisher: American Mathematical Soc. ISBN: 0821891421 Category : Mathematics Languages : en Pages : 305
Book Description
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. ISBN: 1470434911 Category : Functional analysis Languages : en Pages : 290
Book Description
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: P.N. Natarajan Publisher: Springer ISBN: 8132225597 Category : Mathematics Languages : en Pages : 159
Book Description
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: Alain Escassut Publisher: World Scientific ISBN: 9789810222345 Category : Mathematics Languages : en Pages : 408
Book Description
This is probably the first book dedicated to this topic. The behaviour of the analytic elements on an infraconnected set D in K an algebraically closed complete ultrametric field is mainly explained by the circular filters and the monotonous filters on D, especially the T-filters: zeros of the elements, Mittag-Leffler series, factorization, Motzkin factorization, maximum principle, injectivity, algebraic properties of the algebra of the analytic elements on D, problems of analytic extension, factorization into meromorphic products and connections with Mittag-Leffler series. This is applied to the differential equation y'=hy (y, h analytic elements on D), analytic interpolation, injectivity, and to the p-adic Fourier transform.
Author: Alain Escassut Publisher: ISBN: 9781470446765 Category : Electronic books Languages : en Pages : 298
Book Description
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: CRC Press ISBN: 1000191478 Category : Mathematics Languages : en Pages : 220
Book Description
There are excellent books on both functional analysis and summability. Most of them are very terse. In Functional Analysis and Summability, the author makes a sincere attempt for a gentle introduction of these topics to students. In the functional analysis component of the book, the Hahn–Banach theorem, Banach–Steinhaus theorem (or uniform boundedness principle), the open mapping theorem, the closed graph theorem, and the Riesz representation theorem are highlighted. In the summability component of the book, the Silverman–Toeplitz theorem, Schur’s theorem, the Steinhaus theorem, and the Steinhaus-type theorems are proved. The utility of functional analytic tools like the uniform boundedness principle to prove some results in summability theory is also pointed out. Features A gentle introduction of the topics to the students is attempted. Basic results of functional analysis and summability theory and their applications are highlighted. Many examples are provided in the text. Each chapter ends with useful exercises. This book will be useful to postgraduate students, pre-research level students, and research scholars in mathematics. Students of physics and engineering will also find this book useful since topics in the book also have applications in related areas.
Author: W.H. Schikhof Publisher: CRC Press ISBN: 1000145913 Category : Mathematics Languages : en Pages : 419
Book Description
"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."
Author: A.K. Katsaras Publisher: CRC Press ISBN: 9780203908143 Category : Mathematics Languages : en Pages : 340
Book Description
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.
Author: Bertin Diarra
Author: Bertin Diarra
Author: Wilhelmus Hendricus Schikhof
Author: Khodr Shamseddine
Author: Alain Escassut
Author: P.N. Natarajan
Author: Alain Escassut
Author: Alain Escassut
Author: P.N. Natarajan
Author: W.H. Schikhof
Author: A.K. Katsaras