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Author : S. Albeverio,V. M. Shelkovich
Publisher : Cambridge University Press
Page : 369 pages
File Size : 53,8 Mb
Release : 2010-03-18
Category : Mathematics
ISBN : 9780521148566
A wide-ranging 2010 survey of new and important topics in p-adic analysis for researchers and graduate students.
Author : Sergio Albeverio
Publisher : Unknown
Page : 351 pages
File Size : 43,8 Mb
Release : 2010
Category : Distribution (Probability theory)
ISBN : 1139122851
A wide-ranging survey of new and important topics in p-adic analysis for researchers and graduate students.
Author : Sergio Albeverio,A Yu Khrennikov,V M Shelkovich
Publisher : Unknown
Page : 368 pages
File Size : 52,7 Mb
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 1139127772
A wide-ranging 2010 survey of new and important topics in p-adic analysis for researchers and graduate students.
Author : Andrei Y. Khrennikov
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 46,6 Mb
Release : 2013-03-09
Category : Science
ISBN : 9789401583565
Numbers ... , natural, rational, real, complex, p-adic .... What do you know about p-adic numbers? Probably, you have never used any p-adic (nonrational) number before now. I was in the same situation few years ago. p-adic numbers were considered as an exotic part of pure mathematics without any application. I have also used only real and complex numbers in my investigations in functional analysis and its applications to the quantum field theory and I was sure that these number fields can be a basis of every physical model generated by nature. But recently new models of the quantum physics were proposed on the basis of p-adic numbers field Qp. What are p-adic numbers, p-adic analysis, p-adic physics, p-adic probability? p-adic numbers were introduced by K. Hensel (1904) in connection with problems of the pure theory of numbers. The construction of Qp is very similar to the construction of (p is a fixed prime number, p = 2,3,5, ... ,127, ... ). Both these number fields are completions of the field of rational numbers Q. But another valuation 1 . Ip is introduced on Q instead of the usual real valuation 1 . I· We get an infinite sequence of non isomorphic completions of Q : Q2, Q3, ... , Q127, ... , IR = Qoo· These fields are the only possibilities to com plete Q according to the famous theorem of Ostrowsky.
Author : Alain Escassut
Publisher : World Scientific
Page : 559 pages
File Size : 43,8 Mb
Release : 2015-11-27
Category : Mathematics
ISBN : 9789814730112
"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."--
Author : Vasili? Sergeevich Vladimirov,I. V. Volovich,E. I. Zelenov
Publisher : World Scientific
Page : 350 pages
File Size : 51,8 Mb
Release : 1994
Category : Science
ISBN : 9810208804
p-adic numbers play a very important role in modern number theory, algebraic geometry and representation theory. Lately p-adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the non-Archimedean geometry of space-time at small distances.This is the first book to deal with applications of p-adic numbers in theoretical and mathematical physics. It gives an elementary and thoroughly written introduction to p-adic numbers and p-adic analysis with great numbers of examples as well as applications of p-adic numbers in classical mechanics, dynamical systems, quantum mechanics, statistical physics, quantum field theory and string theory.
Author : Nguyen Minh Chuong
Publisher : Springer
Page : 368 pages
File Size : 46,7 Mb
Release : 2018-11-28
Category : Mathematics
ISBN : 9783319774732
This monograph offers a self-contained introduction to pseudodifferential operators and wavelets over real and p-adic fields. Aimed at graduate students and researchers interested in harmonic analysis over local fields, the topics covered in this book include pseudodifferential operators of principal type and of variable order, semilinear degenerate pseudodifferential boundary value problems (BVPs), non-classical pseudodifferential BVPs, wavelets and Hardy spaces, wavelet integral operators, and wavelet solutions to Cauchy problems over the real field and the p-adic field.
Author : Claire C. Ralph,Santiago R. Simanca
Publisher : Cambridge University Press
Page : 146 pages
File Size : 42,7 Mb
Release : 2012-01-26
Category : Mathematics
ISBN : 9781107674141
This complete introduction to the study of arithmetic differential operators over the p-adic integers offers graduate students and researchers an accessible guide to this novel and promising area of mathematics. It starts with the basics and is accessible to anyone with a basic grasp of algebraic number theory.
Author : Vladimir Anashin,Andreĭ I︠U︡rʹevich Khrennikov
Publisher : Walter de Gruyter
Page : 558 pages
File Size : 54,6 Mb
Release : 2009
Category : Mathematics
ISBN : 9783110203004
The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Cear , Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
Author : Anonim
Publisher : Unknown
Page : 296 pages
File Size : 40,7 Mb
Release : 2004
Category : Mathematical analysis
ISBN : UCSC:32106017395101
Author : Dubravka Ban
Publisher : Springer Nature
Page : 219 pages
File Size : 45,6 Mb
Release : 2023-02-11
Category : Mathematics
ISBN : 9783031226847
This book systematically develops the theory of continuous representations on p-adic Banach spaces. Its purpose is to lay the foundations of the representation theory of reductive p-adic groups on p-adic Banach spaces, explain the duality theory of Schneider and Teitelbaum, and demonstrate its applications to continuous principal series. Written to be accessible to graduate students, the book gives a comprehensive introduction to the necessary tools, including Iwasawa algebras, p-adic measures and distributions, p-adic functional analysis, reductive groups, and smooth and algebraic representations. Part 1 culminates with the duality between Banach space representations and Iwasawa modules. This duality is applied in Part 2 for studying the intertwining operators and reducibility of the continuous principal series on p-adic Banach spaces. This monograph is intended to serve both as a reference book and as an introductory text for graduate students and researchers entering the area.
Author : Andreĭ I︠U︡rʹevich Khrennikov,Andrei Yu. Khrennikov,Sergei V. Kozyrev,W. A. Zúñiga-Galindo
Publisher : Cambridge University Press
Page : 255 pages
File Size : 51,9 Mb
Release : 2018-04-26
Category : Mathematics
ISBN : 9781107188822
Provides a novel interdisciplinary perspective on the state of the art of ultrametric pseudodifferential equations and their applications.
Author : Mikhail Kapranov,Sergii Kolyada,Yu. I. Manin,Pieter Moree,Leonid Potyagailo
Publisher : Springer Science & Business Media
Page : 742 pages
File Size : 42,5 Mb
Release : 2008-03-05
Category : Mathematics
ISBN : 3764386088
Alexander Reznikov (1960-2003) was a brilliant and highly original mathematician. This book presents 18 articles by prominent mathematicians and is dedicated to his memory. In addition it contains an influential, so far unpublished manuscript by Reznikov of book length. The book further provides an extensive survey on Kleinian groups in higher dimensions and some articles centering on Reznikov as a person.
Author : Michel Courtieu,Alexei A. Panchishkin
Publisher : Springer
Page : 204 pages
File Size : 53,6 Mb
Release : 2003-12-15
Category : Mathematics
ISBN : 9783540451785
This book, now in its 2nd edition, is devoted to the arithmetical theory of Siegel modular forms and their L-functions. The central object are L-functions of classical Siegel modular forms whose special values are studied using the Rankin-Selberg method and the action of certain differential operators on modular forms which have nice arithmetical properties. A new method of p-adic interpolation of these critical values is presented. An important class of p-adic L-functions treated in the present book are p-adic L-functions of Siegel modular forms having logarithmic growth. The given construction of these p-adic L-functions uses precise algebraic properties of the arithmetical Shimura differential operator. The book will be very useful for postgraduate students and for non-experts looking for a quick approach to a rapidly developing domain of algebraic number theory. This new edition is substantially revised to account for the new explanations that have emerged in the past 10 years of the main formulas for special L-values in terms of arithmetical theory of nearly holomorphic modular forms.
Author : Helge Glöckner,Alain Escassut,Khodr Shamseddine
Publisher : American Mathematical Soc.
Page : 346 pages
File Size : 43,9 Mb
Release : 2016-05-20
Category : Functional analysis
ISBN : 9781470419882
This volume contains the Proceedings of the 13th International Conference on p-adic Functional Analysis, held from August 12–16, 2014, at the University of Paderborn, Paderborn, Germany. The articles included in this book feature recent developments in various areas of non-Archimedean analysis, non-Archimedean functional analysis, representation theory, number theory, non-Archimedean dynamical systems and applications. 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.