Download or read book Analytic Elements in P adic Analysis written by Alain Escassut and published by World Scientific. This book was released on 1995 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Course in p adic Analysis written by Alain M. Robert and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Value Distribution In P adic Analysis written by Alain Escassut and published by World Scientific. This book was released on 2015-11-27 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book P adic Analytic Functions written by Alain Escassut and published by World Scientific. This book was released on 2021-03-17 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Value Distribution in P Adic Analysis written by Alain Escassut and published by World Scientific. This book was released on 2015-11-27 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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."--
Download or read book p adic Functional Analysis written by W.H. Schikhof and published by CRC Press. This book was released on 2020-11-25 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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."
Download or read book p adic Functional Analysis written by W.H. Schikhof and published by CRC Press. This book was released on 2020-11-26 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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."
Download or read book p adic Functional Analysis written by N. De Grande-De Kimpe and published by CRC Press. This book was released on 1999-07-07 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Advances in p adic and Non Archimedean Analysis written by M. Berz and published by American Mathematical Soc.. This book was released on 2010-02-17 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book P Adic Functional Analysis written by A.K. Katsaras and published by CRC Press. This book was released on 2001-07-03 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Advances in Ultrametric Analysis written by Khodr Shamseddine and published by American Mathematical Soc.. This book was released on 2013 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Advances in Ultrametric Analysis written by Alain Escassut and published by American Mathematical Soc.. This book was released on 2018-03-26 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Algebra And Number Theory written by Mohammed Boulagouaz and published by CRC Press. This book was released on 1999-11-09 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book P adic Analysis written by Neal Koblitz and published by Cambridge University Press. This book was released on 1980-11-28 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to recent work in the theory of numbers and its interrelation with algebraic geometry and analysis.
Download or read book P adic Deterministic and Random Dynamics written by Andrei Y. Khrennikov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Ultrametric Banach Algebras written by Alain Escassut and published by World Scientific. This book was released on 2003 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book p adic Numbers p adic Analysis and Zeta Functions written by NEAL Koblitz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes are intended as an introduction to p-adic analysis on the elementary level. For this reason they presuppose as little background as possi ble. Besides about three semesters of calculus, I presume some slight exposure to more abstract mathematics, to the extent that the student won't have an adverse reaction to matrices with entries in a field other than the real numbers, field extensions of the rational numbers, or the notion of a continuous map of topolog ical spaces. The purpose of this book is twofold: to develop some basic ideas of p-adic analysis, and to present two striking applications which, it is hoped, can be as effective pedagogically as they were historically in stimulating interest in the field. The first of these applications is presented in Chapter II, since it only requires the most elementary properties of Q ; this is Mazur's construction by p means of p-adic integration of the Kubota-Leopoldtp-adic zeta-function, which "p-adically interpolates" the values of the Riemann zeta-function at the negative odd integers. My treatment is based on Mazur's Bourbaki notes (unpublished).
