# Ultrametric Calculus

This is an introduction to p-adic analysis which is elementary yet complete and which displays the variety of applications of the subject. Dr Schikhof is able to point out and explain how p-adic and 'real' analysis differ.

Author: W. H. Schikhof

Publisher: Cambridge University Press

ISBN: 9780521032872

Category: Mathematics

Page: 320

View: 349

This is an introduction to p-adic analysis which is elementary yet complete and which displays the variety of applications of the subject. Dr Schikhof is able to point out and explain how p-adic and 'real' analysis differ. This approach guarantees the reader quickly becomes acquainted with this equally 'real' analysis and appreciates its relevance. The reader's understanding is enhanced and deepened by the large number of exercises included throughout; these both test the reader's grasp and extend the text in interesting directions. As a consequence, this book will become a standard reference for professionals (especially in p-adic analysis, number theory and algebraic geometry) and will be welcomed as a textbook for advanced students of mathematics familiar with algebra and analysis.
2007-01-25

W. H. Schikhof, Ultrametric calculus: An introduction to p-adic analysis, Cambridge Studies in Advanced Mathematics, vol. 4, Cambridge University Press, Cambridge, 2006. Reprint of the 1984 original [MR0791759].

Author: Alain Escassut

Publisher: American Mathematical Soc.

ISBN: 9781470434915

Category: Functional analysis

Page: 290

View: 457

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.
2018-03-26

12th International Conference on P-adic Functional Analysis, July 2-6, 2012, University of Manitoba, Winnipeg, Manitoba, ... Ultrametric calculus, Cambridge Studies in Advanced Mathematics, vol. ... An introduction to p-adic analysis.

Author: Khodr Shamseddine

Publisher: American Mathematical Soc.

ISBN: 9780821891421

Category: Mathematics

Page: 291

View: 278

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. The articles included in this book feature recent developments in various areas of non-archimedean analysis: branched values and zeros of the derivative of a $p$-adic meromorphic function, p-adic meromorphic functions $f^{\prime}P^{\prime}(f), g^{\prime}P^{\prime}(g)$ sharing a small function, properties of composition of analytic functions, partial fractional differentiability, morphisms between ultrametric Banach algebras of continuous functions and maximal ideals of finite dimension, the $p$-adic $q$-distributions, Banach spaces over fields with an infinite rank valuation, Grobman-Hartman theorems for diffeomorphisms of Banach spaces over valued fields, integral representations of continuous linear maps on $p$-adic spaces of continuous functions, non-Archimedean operator algebras, generalized Keller spaces over valued fields, proper multiplications on the completion of a totally ordered abelian group, the Grothendieck approximation theory in non-Archimedean functional analysis, generalized power series spaces, measure theory and the study of power series and analytic functions on the Levi-Civita fileds. 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.
2013

# Current Trends in Mathematical Analysis and Its Interdisciplinary Applications

W.H. Schikhof, Ultrametric Calculus: An Introduction to p-Adic Analysis. Cambridge Studies in Advanced Mathematics, vol. 4 (Cambridge University Press, Cambridge, 1984) 28. Y. Simsek, A. Yardimci, Applications on the Apostol-Daehee ...

Author: Hemen Dutta

Publisher: Springer Nature

ISBN: 9783030152420

Category: Mathematics

Page: 909

View: 150

This book explores several important aspects of recent developments in the interdisciplinary applications of mathematical analysis (MA), and highlights how MA is now being employed in many areas of scientific research. Each of the 23 carefully reviewed chapters was written by experienced expert(s) in respective field, and will enrich readers’ understanding of the respective research problems, providing them with sufficient background to understand the theories, methods and applications discussed. The book’s main goal is to highlight the latest trends and advances, equipping interested readers to pursue further research of their own. Given its scope, the book will especially benefit graduate and PhD students, researchers in the applied sciences, educators, and engineers with an interest in recent developments in the interdisciplinary applications of mathematical analysis.
2019-08-23

[176] F. Oort and T. Zink, Families of p-divisible groups with constant Newton polygon, Doc. Math. ... [193] W. H. Schikhof, Ultrametric Calculus: An Introduction to p-adic Analysis, Cambridge Studies in Advanced Math.

Author: Kiran S. Kedlaya

Publisher: Cambridge University Press

ISBN: 9781139489201

Category: Mathematics

Page:

View: 168

Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study.
2010-06-10

p-adic Geometry: Lectures from the 2007 Arizona Winter School, Univ. Lecture Series 45, Amer. Math. Soc., 2008. [361] W.H. Schikhof, Ultrametric Calculus: An Introduction to p-adic Analysis, Cambridge Studies in Advanced Math.

Author: Kiran Kedlaya

Publisher: Cambridge University Press

ISBN: 9781009123341

Category: Mathematics

Page: 420

View: 242

A detailed and unified treatment of $P$-adic differential equations, from the basic principles to the current frontiers of research.
2022-05-31

# Advances in Non Archimedean Analysis

A. M. Robert, A Course in p-adic Analysis, Graduate Texts in Mathematics, Springer-Verlag, New York, 2000. W. H. Schikhof, Ultrametric Calculus: An introduction to p-adic analysis, Cambridge Studies in Advanced Mathematics, Cambridge ...

Author: Jesus Araujo-Gomez

Publisher: American Mathematical Soc.

ISBN: 9780821852910

Category: Mathematics

Page: 280

View: 207

This volume contains papers based on lectures given at the Eleventh International Conference on $p$-adic Functional Analysis, which was held from July 5-9, 2010, in Clermont-Ferrand, France. The articles collected here 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 function spaces, and measure and integration. Other topics discussed in this volume include $p$-adic differential and $q$-difference equations, rational and non-Archimedean analytic functions, the spectrum of some algebras of analytic functions, and maximal ideals of the ultrametric corona algebra.
2011

# Algebraic Methods in Statistics and Probability

T. Satoh, Wiener measures on certain Banach spaces over non-Archimedean local fields, Compositio Math. 93 (1994), 81–108. W.H. Schikhof, Ultrametric Calculus : an Introduction to p-adic Analysis, Cambridge Studies in Advanced ...

Author: Marlos A. G. Viana

Publisher: American Mathematical Soc.

ISBN: 9780821826874

Category: Mathematics

Page: 340

View: 846

Algebraic methods and arguments in statistics and probability are well known, from Gauss' least squares principle through Fisher's method of variance decomposition. The relevance of group-theoretic arguments, for example, became evident in the 1980s. Such techniques continue to be of interest today, along with other developments, such as the use of graph theory in modelling complex stochastic systems.This volume is based on lectures presented at the AMS Special Session on Algebraic Methods and Statistics held at the University of Notre Dame (Indiana) and on contributed articles solicited for this volume. The articles are intended to foster communication between representatives of the diverse scientific areas in which these functions are utilized and to further the trend of utilizing algebraic methods in the areas of statistics and probability. This is one of few volumes devoted to the subject of algebraic methods in statistics and probability. The wide range of topics covered in this volume demonstrates the vigorous level of research and opportunities ongoing in these areas.
2001

# Fractal Geometry and Dynamical Systems in Pure and Applied Mathematics Fractals in pure mathematics

198, Springer-Verlag, New York, 2000. MR1760253 (2001g:11182) Wilhelmus H. Schikhof, Ultrametric Calculus: An introduction to p-adic analysis, Cambridge Studies in Advanced Mathematics, vol. 4, Cambridge University Press, Cambridge, ...

Author: David Carfi

Publisher: American Mathematical Soc.

ISBN: 9780821891476

Category: Mathematics

Page: 399

View: 249

This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoit Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry (and some aspects of dynamical systems) in pure mathematics. Also included are articles discussing a variety of connections of fractal geometry with other fields of mathematics, including probability theory, number theory, geometric measure theory, partial differential equations, global analysis on non-smooth spaces, harmonic analysis and spectral geometry. The companion volume (Contemporary Mathematics, Volume 601) focuses on applications of fractal geometry and dynamical systems to other sciences, including physics, engineering, computer science, economics, and finance.
2013-10-22

# Trends in Biomathematics Modeling Cells Flows Epidemics and the Environment

R. Rammal, G. Toulouse, M.A. Virasoro, Ultrametricity for physicists. Rev. Mod. Phys. 58, 765–788 (1986) 20. W.H. Schikhof, Ultrametric calculus: an introduction to p-Adic analysis, in Cambridge Studies in Advanced Mathematics ...

Author: Rubem P. Mondaini

Publisher: Springer Nature

ISBN: 9783030463069

Category: Mathematics

Page: 425

View: 243