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Banach Algebras Of Ultrametric Functions


Banach Algebras Of Ultrametric Functions
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Banach Algebras Of Ultrametric Functions


Banach Algebras Of Ultrametric Functions
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Author : Alain Escassut
language : en
Publisher: World Scientific
Release Date : 2022-04-08

Banach Algebras Of Ultrametric Functions written by Alain Escassut and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-08 with Mathematics categories.


This book examines ultrametric Banach algebras in general. It begins with algebras of continuous functions, and looks for maximal and prime ideals in connections with ultrafilters on the set of definition. The multiplicative spectrum has shown to be indispensable in ultrametric analysis and is described in the general context and then, in various cases of Banach algebras.Applications are made to various kind of functions: uniformly continuous functions, Lipschitz functions, strictly differentiable functions, defined in a metric space. Analytic elements in an algebraically closed complete field (due to M Krasner) are recalled with most of their properties linked to T-filters and applications to their Banach algebras, and to the ultrametric holomorphic functional calculus, with applications to spectral properties. The multiplicative semi-norms of Krasner algebras are characterized by circular filters with a metric and an order that are examined.The definition of the theory of affinoid algebras due to J Tate is recalled with all the main algebraic properties (including Krasner-Tate algebras). The existence of idempotents associated to connected components of the multiplicative spectrum is described.



Ultrametric Banach Algebras


Ultrametric Banach Algebras
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Author : Alain Escassut
language : en
Publisher: World Scientific
Release Date : 2003-03-04

Ultrametric Banach Algebras written by Alain Escassut and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-04 with Mathematics categories.


In this book, ultrametric Banach algebras are studied with the help of topological considerations, properties from affinoid algebras, and circular filters which characterize absolute values on polynomials and make a nice tree structure. The Shilov boundary does exist for normed ultrametric algebras.In uniform Banach algebras, the spectral norm is equal to the supremum of all continuous multiplicative seminorms whose kernel is a maximal ideal. Two different such seminorms can have the same kernel. Krasner-Tate algebras are characterized among Krasner algebras, affinoid algebras, and ultrametric Banach algebras. Given a Krasner-Tate algbebra A=K{t}[x], the absolute values extending the Gauss norm from K{t} to A are defined by the elements of the Shilov boundary of A.



Advances In Ultrametric Analysis


Advances In Ultrametric Analysis
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Author : Alain Escassut
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-03-26

Advances In Ultrametric Analysis written by Alain Escassut and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-26 with Mathematics categories.


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.



Fourier Analysis On Number Fields


Fourier Analysis On Number Fields
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Author : Dinakar Ramakrishnan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Fourier Analysis On Number Fields written by Dinakar Ramakrishnan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.


This book grew out of notes from several courses that the first author has taught over the past nine years at the California Institute of Technology, and earlier at the Johns Hopkins University, Cornell University, the University of Chicago, and the University of Crete. Our general aim is to provide a modern approach to number theory through a blending of complementary algebraic and analytic perspectives, emphasizing harmonic analysis on topological groups. Our more particular goal is to cover Jolm Tate's visionary thesis, giving virtually all of the necessary analytic details and topological preliminaries-technical prereq uisites that are often foreign to the typical, more algebraically inclined number theorist. Most of the existing treatments of Tate's thesis, including Tate's own, range from terse to cryptic; our intent is to be more leisurely, more comprehen sive, and more comprehensible. To this end we have assembled material that has admittedly been treated elsewhere, but not in a single volume with so much detail and not with our particular focus. We address our text to students who have taken a year of graduate-level courses in algebra, analysis, and topology. While our choice of objects and methods is naturally guided by the specific mathematical goals of the text, our approach is by no means narrow. In fact, the subject matter at hand is germane not only to budding number theorists, but also to students of harmonic analysis or the representation theory of Lie groups.



Ultrametric Banach Algebras


Ultrametric Banach Algebras
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Author : Alain Escassut
language : en
Publisher: World Scientific
Release Date : 2003

Ultrametric Banach Algebras written by Alain Escassut and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.


In this book, ultrametric Banach algebras are studied with the help of topological considerations, properties from affinoid algebras, and circular filters which characterize absolute values on polynomials and make a nice tree structure. The Shilov boundary does exist for normed ultrametric algebras. In uniform Banach algebras, the spectral norm is equal to the supremum of all continuous multiplicative seminorms whose kernel is a maximal ideal. Two different such seminorms can have the same kernel. KrasnerTate algebras are characterized among Krasner algebras, affinoid algebras, and ultrametric Banach algebras. Given a KrasnerTate algbebra A=K{t}[x], the absolute values extending the Gauss norm from K{t} to A are defined by the elements of the Shilov boundary of A.



Advances In Non Archimedean Analysis


Advances In Non Archimedean Analysis
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Author : Jesus Araujo-Gomez
language : en
Publisher: American Mathematical Soc.
Release Date : 2011

Advances In Non Archimedean Analysis written by Jesus Araujo-Gomez and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.


These collected articles 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 functions spaces, and measure and integration.



P Adic Functional Analysis


P Adic Functional Analysis
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Author : W.H. Schikhof
language : en
Publisher: CRC Press
Release Date : 2020-11-25

P Adic Functional Analysis written by W.H. Schikhof and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-25 with Mathematics categories.


"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."



Advances In Algebra And Combinatorics


Advances In Algebra And Combinatorics
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Author : K. P. Shum
language : en
Publisher: World Scientific
Release Date : 2008

Advances In Algebra And Combinatorics written by K. P. Shum and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.


This volume is a compilation of lectures on algebras and combinatorics presented at the Second International Congress in Algebra and Combinatorics. It reports on not only new results, but also on open problems in the field. The proceedings volume is useful for graduate students and researchers in algebras and combinatorics. Contributors include eminent figures such as V Artamanov, L Bokut, J Fountain, P Hilton, M Jambu, P Kolesnikov, Li Wei and K Ueno.



Algebra And Galois Theories


Algebra And Galois Theories
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Author : Régine Douady
language : en
Publisher: Springer Nature
Release Date : 2020-07-13

Algebra And Galois Theories written by Régine Douady and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-13 with Mathematics categories.


Galois theory has such close analogies with the theory of coverings that algebraists use a geometric language to speak of field extensions, while topologists speak of "Galois coverings". This book endeavors to develop these theories in a parallel way, starting with that of coverings, which better allows the reader to make images. The authors chose a plan that emphasizes this parallelism. The intention is to allow to transfer to the algebraic framework of Galois theory the geometric intuition that one can have in the context of coverings. This book is aimed at graduate students and mathematicians curious about a non-exclusively algebraic view of Galois theory.



Analysis Probability Applications And Computation


Analysis Probability Applications And Computation
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Author : Karl‐Olof Lindahl
language : en
Publisher: Springer
Release Date : 2019-04-29

Analysis Probability Applications And Computation written by Karl‐Olof Lindahl and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-29 with Mathematics categories.


This book is a collection of short papers from the 11th International ISAAC Congress 2017 in Växjö, Sweden. The papers, written by the best international experts, are devoted to recent results in mathematics with a focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on the current research in mathematical analysis and its various interdisciplinary applications.