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P Adic Analysis Compared With Real 1 E Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of P Adic Analysis Compared With Real 1 E book. This book definitely worth reading, it is an incredibly well-written.
Author : Svetlana Katok,Svetlana
Publisher : Unknown
Page : 152 pages
File Size : 44,6 Mb
Release : 2007
Category : Electronic
ISBN : 0821852248
Author : Svetlana Katok
Publisher : American Mathematical Soc.
Page : 152 pages
File Size : 40,5 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821842201
The book gives an introduction to $p$-adic numbers from the point of view of number theory, topology, and analysis. Compared to other books on the subject, its novelty is both a particularly balanced approach to these three points of view and an emphasis on topics accessible to undergraduates. In addition, several topics from real analysis and elementary topology which are not usually covered in undergraduate courses (totally disconnected spaces and Cantor sets, points of discontinuity of maps and the Baire Category Theorem, surjectivity of isometries of compact metric spaces) are also included in the book. They will enhance the reader's understanding of real analysis and intertwine the real and $p$-adic contexts of the book. The book is based on an advanced undergraduate course given by the author. The choice of the topic was motivated by the internal beauty of the subject of $p$-adic analysis, an unusual one in the undergraduate curriculum, and abundant opportunities to compare it with its much more familiar real counterpart. The book includes a large number of exercises. Answers, hints, and solutions for most of them appear at the end of the book. Well written, with obvious care for the reader, the book can be successfully used in a topic course or for self-study.
Author : Svetlana Katok
Publisher : American Mathematical Soc.
Page : 152 pages
File Size : 54,9 Mb
Release : 2007
Category : Mathematics
ISBN : 1470421488
The book gives an introduction to $p$-adic numbers from the point of view of number theory, topology, and analysis. Compared to other books on the subject, its novelty is both a particularly balanced approach to these three points of view and an emphasis on topics accessible to undergraduates. In addition, several topics from real analysis and elementary topology which are not usually covered in undergraduate courses (totally disconnected spaces and Cantor sets, points of discontinuity of maps and the Baire Category Theorem, surjectivity of isometries of compact metric spaces) are also included in the book. They will enhance the reader's understanding of real analysis and intertwine the real and $p$-adic contexts of the book. The book is based on an advanced undergraduate course given by the author. The choice of the topic was motivated by the internal beauty of the subject of $p$-adic analysis, an unusual one in the undergraduate curriculum, and abundant opportunities to compare it with its much more familiar real counterpart. The book includes a large number of exercises. Answers, hints, and solutions for most of them appear at the end of the book. Well written, with obvious care for the reader, the book can be successfully used in a topic course or for self-study.
Author : Alain M. Robert
Publisher : Springer Science & Business Media
Page : 451 pages
File Size : 41,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475732542
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.
Author : Karl‐Olof Lindahl,Torsten Lindström,Luigi G. Rodino,Joachim Toft,Patrik Wahlberg
Publisher : Springer
Page : 568 pages
File Size : 49,6 Mb
Release : 2019-04-29
Category : Mathematics
ISBN : 9783030044596
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.
Author : Vasili? Sergeevich Vladimirov,I. V. Volovich,E. I. Zelenov
Publisher : World Scientific
Page : 350 pages
File Size : 55,6 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 : Biswaranjan Behera,Qaiser Jahan
Publisher : Springer Nature
Page : 345 pages
File Size : 41,5 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9789811678813
This book discusses the theory of wavelets on local fields of positive characteristic. The discussion starts with a thorough introduction to topological groups and local fields. It then provides a proof of the existence and uniqueness of Haar measures on locally compact groups. It later gives several examples of locally compact groups and describes their Haar measures. The book focuses on multiresolution analysis and wavelets on a local field of positive characteristic. It provides characterizations of various functions associated with wavelet analysis such as scaling functions, wavelets, MRA-wavelets and low-pass filters. Many other concepts which are discussed in details are biorthogonal wavelets, wavelet packets, affine and quasi-affine frames, MSF multiwavelets, multiwavelet sets, generalized scaling sets, scaling sets, unconditional basis properties of wavelets and shift invariant spaces.
Author : Francesco Baldassari,Siegfried Bosch,Bernard Dwork
Publisher : Springer
Page : 388 pages
File Size : 42,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540469063
Author : Neal Koblitz
Publisher : Cambridge University Press
Page : 171 pages
File Size : 52,5 Mb
Release : 1980-11-28
Category : Mathematics
ISBN : 9780521280600
An introduction to recent work in the theory of numbers and its interrelation with algebraic geometry and analysis.
Author : Alain Escassut
Publisher : World Scientific
Page : 404 pages
File Size : 44,8 Mb
Release : 1995-10-18
Category : Mathematics
ISBN : 9789814500524
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. Contents:Absolute Values and NormsInfraconnected SetsMonotonous and Circular FiltersUltrametric Absolute Values and Valuation Functions υ(h,μ) on K(x)Hensel LemmaThe Analytic ElementsFactorization of Analytic ElementsThe Mittage–Leffler TheoremDerivative of Analytic ElementsElements Vanishing Along a FilterQuasi-Minorated ElementsAnalytic Elements Meromorphic in a HoleMotzkin FactorizationMaximum in a Circle with HolesT-Filters and T-SequencesIntegrally Closed Algebras H(D)Absolute Values in Algebras H(D)Idempotent T-SequencesAlgebra H(D)/I0(F)Injectivity, Mittag–Leffler Series and Motzkin ProductsGeneralities on the Differential Equation y'=fy in H(D)The Equation y'=fy in Zero Residue Characteristicand other papers Readership: Mathematicians. keywords:p-Adic Fields;Multiplicative Semi-Norms;Ultrametric Analytic Functions;Analytic Elements;T-Filters;Ideals;Principal Ideal Rings
Author : Neal Koblitz
Publisher : Springer Science & Business Media
Page : 163 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461211129
The first edition of this work has become the standard introduction to the theory of p-adic numbers at both the advanced undergraduate and beginning graduate level. This second edition includes a deeper treatment of p-adic functions in Ch. 4 to include the Iwasawa logarithm and the p-adic gamma-function, the rearrangement and addition of some exercises, the inclusion of an extensive appendix of answers and hints to the exercises, as well as numerous clarifications.
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 51,5 Mb
Release : 2024-06-29
Category : Electronic
ISBN : 9789814476003
Author : V S Vladimirov,I V Volovich,E I Zelenov
Publisher : World Scientific
Page : 340 pages
File Size : 42,9 Mb
Release : 1994-04-28
Category : Science
ISBN : 9789814505765
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. Contents:Analysis on the Field p-Adic Numbers:The Field of p-Adic NumbersAnalytic FunctionsAdditive and Multiplicative CharactersIntegration TheoryThe Gaussian IntegralsGeneralized FunctionsConvolution and the Fourier TransformationHomogeneous Generalized FunctionsPseudo-Differential Operators on the Field of p-Adic Numbers:The Operator D?p-Adic Schrodinger Operatorsp-Adic Quantum Theory:p-Adic Quantum MechanicsSpectral Theory in p-Adic Quantum MechanicsWeyl Systems. Infinite Dimensional Casep-Adic Stringsq-Analysis (Quantum Groups) and p-Adic AnalysisStochastic Processes Over the Field of p-Adic Numbers Readership: Students, postgraduates, mathematical physicists, mathematicians and physicists. keywords:Distribution Theory à la Bruhat;Planck Scale;p-Adic Analysis;Gaussian Integrals;Fourier Theory;Convolution of Generalized Functions;p-Adic Quantum Mechanics;Spectral Theory;Weyl Systems;p-Adic Strings;Quantum Groups;q-Analysis;Stochastic Processes
Author : Alain Escassut
Publisher : World Scientific
Page : 559 pages
File Size : 50,7 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 : Svetlana Katok,A. B. Sossinsky,Serge Tabachnikov
Publisher : American Mathematical Soc.
Page : 326 pages
File Size : 54,5 Mb
Release : 2024-06-29
Category : Mathematics
ISBN : 0821872583
This book results from a unique and innovative program at Pennsylvania State University. Under the program, the ''best of the best'' students nationwide are chosen to study challenging mathematical areas under the guidance of experienced mathematicians. This program, Mathematics Advanced Study Semesters (MASS), offers an unparalleled opportunity for talented undergraduate students who are serious in the pursuit of mathematical knowledge. This volume represents various aspects of the MASS program over its six-year existence, including core courses, summer courses, students' research, and colloquium talks. The book is most appropriate for college professors of mathematics who work with bright and eager undergraduate and beginning graduate students, for such students who want to expand their mathematical horizons, and for everyone who loves mathematics and wants to learn more interesting and unusual material. The first half of the book contains lecture notes of nonstandard courses. A text for a semester-long course on $p$-adic analysis is centered around contrasts and similarities with its real counterpart. A shorter text focuses on a classical area of interplay between geometry, algebra and number theory (continued fractions, hyperbolic geometry and quadratic forms). Also provided are detailed descriptions of two innovative courses, one on geometry and the other on classical mechanics. These notes constitute what one may call the skeleton of a course, leaving the instructor ample room for innovation and improvisation. The second half of the book contains a large collection of essays on a broad spectrum of exciting topics from Hilbert's Fourth Problem to geometric inequalities and minimal surfaces, from mathematical billiards to fractals and tilings, from unprovable theorems to the classification of finite simple groups and lexicographic codes.
