Analytic Elements In P Adic Analysis

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Analytic Elements in P-adic Analysis

Alain Escassut
Analytic Elements in P adic Analysis Book PDF

Author : Alain Escassut
Publisher : World Scientific
Page : 408 pages
File Size : 53,5 Mb
Release : 1995
Category : Mathematics
ISBN : 9810222343

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Analytic Elements in P-adic Analysis by Alain Escassut Pdf

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.

A Course in p-adic Analysis

Alain M. Robert
A Course in p adic Analysis Book PDF

Author : Alain M. Robert
Publisher : Springer Science & Business Media
Page : 451 pages
File Size : 53,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475732542

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A Course in p-adic Analysis by Alain M. Robert Pdf

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.

P-adic Analytic Functions

Alain Escassut
P adic Analytic Functions Book PDF

Author : Alain Escassut
Publisher : World Scientific
Page : 349 pages
File Size : 52,8 Mb
Release : 2021-03-17
Category : Mathematics
ISBN : 9789811226236

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P-adic Analytic Functions by Alain Escassut Pdf

P-adic Analytic Functions describes the definition and properties of p-adic analytic and meromorphic functions in a complete algebraically closed ultrametric field.Various properties of p-adic exponential-polynomials are examined, such as the Hermite-Lindemann theorem in a p-adic field, with a new proof. The order and type of growth for analytic functions are studied, in the whole field and inside an open disk. P-adic meromorphic functions are studied, not only on the whole field but also in an open disk and on the complemental of an open disk, using Motzkin meromorphic products. Finally, the p-adic Nevanlinna theory is widely explained, with various applications. Small functions are introduced with results of uniqueness for meromorphic functions. The question of whether the ring of analytic functions—in the whole field or inside an open disk—is a Bezout ring is also examined.

Value Distribution in P-Adic Analysis

Alain Escassut
Value Distribution in P Adic Analysis Book PDF

Author : Alain Escassut
Publisher : World Scientific
Page : 559 pages
File Size : 45,5 Mb
Release : 2015-11-27
Category : Mathematics
ISBN : 9789814730112

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Value Distribution in P-Adic Analysis by Alain Escassut Pdf

"The book first explains the main properties of analytic functions in order to use them in the study of various problems in p-adic value distribution. Certain properties of p-adic transcendental numbers are examined such as order and type of transcendence, with problems on p-adic exponentials. Lazard's problem for analytic functions inside a disk is explained. P-adic meromorphics are studied. Sets of range uniqueness in a p-adic field are examined. The ultrametric Corona problem is studied. Injective analytic elements are characterized. The p-adic Nevanlinna theory is described and many applications are given: p-adic Hayman conjecture, Picard's values for derivatives, small functions, branched values, growth of entire functions, problems of uniqueness, URSCM and URSIM, functions of uniqueness, sharing value problems, Nevanlinna theory in characteristic p>0, p-adic Yosida's equation."--

Value Distribution in p-adic Analysis

Alain Escassut
Value Distribution in p adic Analysis Book PDF

Author : Alain Escassut
Publisher : World Scientific
Page : 600 pages
File Size : 54,6 Mb
Release : 2015-11-27
Category : Mathematics
ISBN : 9789814730129

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Value Distribution in p-adic Analysis by Alain Escassut Pdf

' The book first explains the main properties of analytic functions in order to use them in the study of various problems in p-adic value distribution. Certain properties of p-adic transcendental numbers are examined such as order and type of transcendence, with problems on p-adic exponentials. Lazard''s problem for analytic functions inside a disk is explained. P-adic meromorphics are studied. Sets of range uniqueness in a p-adic field are examined. The ultrametric Corona problem is studied. Injective analytic elements are characterized. The p-adic Nevanlinna theory is described and many applications are given: p-adic Hayman conjecture, Picard''s values for derivatives, small functions, branched values, growth of entire functions, problems of uniqueness, URSCM and URSIM, functions of uniqueness, sharing value problems, Nevanlinna theory in characteristic p>0, p-adic Yosida''s equation. Contents: Ultrametric FieldsHensel LemmaSpherically Complete ExtensionsAnalytic ElementsPower and Laurent SeriesFactorization of Analytic ElementsDerivative of Analytic ElementsVanishing along a Monotonous FilterMaximum PrincipleQuasi-Invertible Analytic ElementsMeromorphic FunctionsThe Corona Problem on Ab(d(0,1‾))Applications to CurvesGrowth of the Derivative of an Entire FunctionRational Decomposition for Entire Functionsand other papers Readership: Graduate students and researchers interested in p-adic analysis. Keywords:p-Adic;Transcendental Numbers;Meromorphic;Nevalinna Theory'

p-adic Functional Analysis

W.H. Schikhof,C. Perez-Garcia,Jerzy Kakol
p adic Functional Analysis Book PDF

Author : W.H. Schikhof,C. Perez-Garcia,Jerzy Kakol
Publisher : CRC Press
Page : 419 pages
File Size : 41,6 Mb
Release : 2020-11-26
Category : Mathematics
ISBN : 9781000145915

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p-adic Functional Analysis by W.H. Schikhof,C. Perez-Garcia,Jerzy Kakol Pdf

"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."

p-adic Functional Analysis

N. De Grande-De Kimpe,Jerzy Kakol,C. Perez-Garcia
p adic Functional Analysis Book PDF

Author : N. De Grande-De Kimpe,Jerzy Kakol,C. Perez-Garcia
Publisher : CRC Press
Page : 350 pages
File Size : 55,5 Mb
Release : 1999-07-07
Category : Mathematics
ISBN : 0824782542

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p-adic Functional Analysis by N. De Grande-De Kimpe,Jerzy Kakol,C. Perez-Garcia Pdf

A presentation of results in p-adic Banach spaces, spaces over fields with an infinite rank valuation, Frechet (and locally convex) spaces with Schauder bases, function spaces, p-adic harmonic analysis, and related areas. It showcases research results in functional analysis over nonarchimedean valued complete fields. It explores spaces of continuous functions, isometries, Banach Hopf algebras, summability methods, fractional differentiation over local fields, and adelic formulas for gamma- and beta-functions in algebraic number theory.

P-Adic Functional Analysis

A.K. Katsaras,W.H. Schikhof,L. Van Hamme
P Adic Functional Analysis Book PDF

Author : A.K. Katsaras,W.H. Schikhof,L. Van Hamme
Publisher : CRC Press
Page : 340 pages
File Size : 55,8 Mb
Release : 2001-07-03
Category : Mathematics
ISBN : 0203908147

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P-Adic Functional Analysis by A.K. Katsaras,W.H. Schikhof,L. Van Hamme Pdf

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.

Advances in Ultrametric Analysis

Alain Escassut,Cristina Perez-Garcia,Khodr Shamseddine
Advances in Ultrametric Analysis Book PDF

Author : Alain Escassut,Cristina Perez-Garcia,Khodr Shamseddine
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 48,5 Mb
Release : 2018-03-26
Category : Functional analysis
ISBN : 9781470434915

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Advances in Ultrametric Analysis by Alain Escassut,Cristina Perez-Garcia,Khodr Shamseddine Pdf

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.

Ultrametric Banach Algebras

Alain Escassut
Ultrametric Banach Algebras Book PDF

Author : Alain Escassut
Publisher : World Scientific
Page : 291 pages
File Size : 41,6 Mb
Release : 2003
Category : Mathematics
ISBN : 9789812381941

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Ultrametric Banach Algebras by Alain Escassut Pdf

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.

Algebra And Number Theory

Mohammed Boulagouaz,Jean-Pierre Tignol
Algebra And Number Theory Book PDF

Author : Mohammed Boulagouaz,Jean-Pierre Tignol
Publisher : CRC Press
Page : 306 pages
File Size : 46,5 Mb
Release : 1999-11-09
Category : Mathematics
ISBN : 0203903889

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Algebra And Number Theory by Mohammed Boulagouaz,Jean-Pierre Tignol Pdf

This study demonstrates the key manipulations surrounding Brauer groups, graded rings, group representations, ideal classes of number fields, p-adic differential equations, and rationality problems of invariant fields - displaying a command of the most advanced methods in algebra. It describes new developments in noncommutative valuation theory and

P-adic Deterministic and Random Dynamics

Andrei Y. Khrennikov,Marcus Nilsson
P adic Deterministic and Random Dynamics Book PDF

Author : Andrei Y. Khrennikov,Marcus Nilsson
Publisher : Springer Science & Business Media
Page : 279 pages
File Size : 40,5 Mb
Release : 2013-03-14
Category : Science
ISBN : 9781402026607

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P-adic Deterministic and Random Dynamics by Andrei Y. Khrennikov,Marcus Nilsson Pdf

This book provides an overview of the theory of p-adic (and more general non-Archimedean) dynamical systems. The main part of the book is devoted to discrete dynamical systems. It presents a model of probabilistic thinking on p-adic mental space based on ultrametric diffusion. Coverage also details p-adic neural networks and their applications to cognitive sciences: learning algorithms, memory recalling.

Advances in $p$-adic and Non-Archimedean Analysis

M. Berz,Khodr Shamseddine
Advances in p adic and Non Archimedean Analysis Book PDF

Author : M. Berz,Khodr Shamseddine
Publisher : American Mathematical Soc.
Page : 281 pages
File Size : 50,5 Mb
Release : 2010-02-17
Category : Mathematics
ISBN : 9780821847404

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Advances in $p$-adic and Non-Archimedean Analysis by M. Berz,Khodr Shamseddine Pdf

This volume contains the proceedings of the Tenth International Conference on $p$-adic and Non-Archimedean Analysis, held at Michigan State University in East Lansing, Michigan, on June 30-July 3, 2008. This volume contains a kaleidoscope of papers based on several of the more important talks presented at the meeting. It provides a cutting-edge connection to some of the most important recent developments in the field. Through a combination of survey papers, research articles, and extensive references to earlier work, this volume allows the reader to quickly gain an overview of current activity in the field and become acquainted with many of the recent sub-branches of its development.

Advances in Ultrametric Analysis

Khodr Shamseddine
Advances in Ultrametric Analysis Book PDF

Author : Khodr Shamseddine
Publisher : American Mathematical Soc.
Page : 305 pages
File Size : 43,7 Mb
Release : 2013
Category : Mathematics
ISBN : 9780821891421

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Advances in Ultrametric Analysis by Khodr Shamseddine Pdf

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.

Stochastic Analysis and Related Topics VI

Laurent Decreusefond
Stochastic Analysis and Related Topics VI Book PDF

Author : Laurent Decreusefond
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 49,7 Mb
Release : 1998-12-18
Category : Mathematics
ISBN : 0817640185

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Stochastic Analysis and Related Topics VI by Laurent Decreusefond Pdf

This volume contains the contributions of the participants of the Sixth Oslo-Silivri Workshop on Stochastic Analysis, held in Geilo from July 29 to August 6, 1996. There are two main lectures - Stochastic Differential Equations with Memory, by S.E. A. Mohammed, - Backward SDE's and Viscosity Solutions of Second Order Semilinear PDE's, by E. Pardoux. The main lectures are presented at the beginning of the volume. There is also a review paper at the third place about the stochastic calculus of variations on Lie groups. The contributing papers vary from SPDEs to Non-Kolmogorov type probabilistic models. We would like to thank - VISTA, a research cooperation between Norwegian Academy of Sciences and Letters and Den Norske Stats Oljeselskap (Statoil), - CNRS, Centre National de la Recherche Scientifique, - The Department of Mathematics of the University of Oslo, - The Ecole Nationale Superieure des Telecommunications, for their financial support. L. Decreusefond J. Gjerde B. 0ksendal A.S. Ustunel PARTICIPANTS TO THE 6TH WORKSHOP ON STOCHASTIC ANALYSIS Vestlia H yfjellshotell, Geilo, Norway, July 28 -August 4, 1996. E-mail: [email protected] Aureli ALABERT Departament de Matematiques Laurent DECREUSEFOND Universitat Autonoma de Barcelona Ecole Nationale Superieure des Telecom- 08193-Bellaterra munications CATALONIA (Spain) Departement Reseaux E-mail: [email protected] 46, rue Barrault Halvard ARNTZEN 75634 Paris Cedex 13 Dept. of Mathematics FRANCE University of Oslo E-mail: [email protected] Box 1053 Blindern Laurent DENIS N-0316 Oslo C.M.I.