Alain Escassut's Books

Value Distribution In P-adic Analysis

By: Alain Escassut

Write a review Read reviews Take a Quiz Solve Book Puzzle

Value Distribution In P-adic Analysis

By: Alain Escassut

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.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

559

Publisher

World Scientific

Published Date

ISBN 10

9814730122

ISBN 13

9789814730129

Ultrametric Functional Analysis

Seventh International Conference on P-Adic Functional Analysis, June 17-21, 2002, University of Nijmegen, the Netherlands

By: Wilhelmus Hendricus Schikhof,C. Perez-Garcia,Alain Escassut

Write a review Read reviews Take a Quiz Solve Book Puzzle

Ultrametric Functional Analysis

Seventh International Conference on P-Adic Functional Analysis, June 17-21, 2002, University of Nijmegen, the Netherlands

By: Wilhelmus Hendricus Schikhof,C. Perez-Garcia,Alain Escassut

This volume contains research articles based on lectures given at the Seventh International Conference on $p$-adic Functional Analysis. The articles, written by leading international experts, provide a complete overview of the latest contributions in basic functional analysis (Hilbert and Banach spaces, locally convex spaces, orthogonality, inductive limits, spaces of continuous functions, strict topologies, operator theory, automatic continuity, measure and integrations, Banach and topological algebras, summability methods, and ultrametric spaces), analytic functions (meromorphic functions, roots of rational functions, characterization of injective holomorphic functions, and Gelfand transforms in algebras of analytic functions), differential equations, Banach-Hopf algebras, Cauchy theory of Levi-Civita fields, finite differences, weighted means, $p$-adic dynamical systems, and non-Archimedean probability theory and stochastic processes. The book is written for graduate students and research mathematicians. It also would make a good reference source for those in related areas, such as classical functional analysis, complex analytic functions, probability theory, dynamical systems, orthomodular spaces, number theory, and representations of $p$-adic groups.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

434

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821833200

ISBN 13

9780821833209

Banach Algebras Of Ultrametric Functions

By: Alain Escassut

Write a review Read reviews Take a Quiz Solve Book Puzzle

Banach Algebras Of Ultrametric Functions

By: Alain Escassut

This book examines ultrametric Banach algebras in general. It begins with algebras of continuous functions, and looks for maximal and prime ideals in connections with ultrafilters on the set of definition. The multiplicative spectrum has shown to be indispensable in ultrametric analysis and is described in the general context and then, in various cases of Banach algebras.Applications are made to various kind of functions: uniformly continuous functions, Lipschitz functions, strictly differentiable functions, defined in a metric space. Analytic elements in an algebraically closed complete field (due to M Krasner) are recalled with most of their properties linked to T-filters and applications to their Banach algebras, and to the ultrametric holomorphic functional calculus, with applications to spectral properties. The multiplicative semi-norms of Krasner algebras are characterized by circular filters with a metric and an order that are examined.The definition of the theory of affinoid algebras due to J Tate is recalled with all the main algebraic properties (including Krasner-Tate algebras). The existence of idempotents associated to connected components of the multiplicative spectrum is described.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

323

Publisher

World Scientific

Published Date

ISBN 10

9811251673

ISBN 13

9789811251672

Analytic Elements in P-adic Analysis

By: Alain Escassut

Write a review Read reviews Take a Quiz Solve Book Puzzle

Analytic Elements in P-adic Analysis

By: Alain Escassut

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.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

408

Publisher

World Scientific

Published Date

ISBN 10

9810222343

ISBN 13

9789810222345

A Course in p-adic Analysis

By: Alain M. Robert

Write a review Read reviews Take a Quiz Solve Book Puzzle

A Course in p-adic Analysis

By: Alain M. Robert

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.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

451

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1475732546

ISBN 13

9781475732542

Ultrametric Banach Algebras

By: Alain Escassut

Write a review Read reviews Take a Quiz Solve Book Puzzle

Ultrametric Banach Algebras

By: Alain Escassut

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. KrasnerOCoTate algebras are characterized among Krasner algebras, affinoid algebras, and ultrametric Banach algebras. Given a KrasnerOCoTate 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 . Contents: Tree Structure; Ultrametric Absolute Values; Hensel Lemma; Circular Filters; Analytic Elements; Holomorphic Properties on Infraconnected Sets; Analytic Elements on Classic Partitions; Holomorphic Functional Calculus; Definition of Affinoid Algebras; Jacobson Radical of Affinoid Algebras; Separable Fields; KrasnerOCoTate Algebras; Universal Generators in Tate Algebras; Associated Idempotents; and other topics. Readership: Graduate students and researchers in ultrametric functional analysis, number theory and dynamical systems.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

291

Publisher

World Scientific

Published Date

ISBN 10

9812775609

ISBN 13

9789812775603

Banach Algebras Of Ultrametric Functions

By: Alain Escassut

Write a review Read reviews Take a Quiz Solve Book Puzzle

Banach Algebras Of Ultrametric Functions

By: Alain Escassut

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

323

Publisher

World Scientific

Published Date

ISBN 10

9811251673

ISBN 13

9789811251672

Value Distribution in P-Adic Analysis

By: Alain Escassut

Write a review Read reviews Take a Quiz Solve Book Puzzle

Value Distribution in P-Adic Analysis

By: Alain Escassut

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

559

Publisher

World Scientific

Published Date

ISBN 10

9814730114

ISBN 13

9789814730112

P-adic Analytic Functions

By: Alain Escassut

Write a review Read reviews Take a Quiz Solve Book Puzzle

P-adic Analytic Functions

By: Alain Escassut

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.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

349

Publisher

World Scientific

Published Date

ISBN 10

9811226237

ISBN 13

9789811226236

Analytic Elements in P-adic Analysis

By: Alain Escassut

Write a review Read reviews Take a Quiz Solve Book Puzzle

Analytic Elements in P-adic Analysis

By: Alain Escassut

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

408

Publisher

World Scientific

Published Date

ISBN 10

9810222343

ISBN 13

9789810222345

Ultrametric Functional Analysis

Seventh International Conference on P-Adic Functional Analysis, June 17-21, 2002, University of Nijmegen, the Netherlands

By: Wilhelmus Hendricus Schikhof,C. Perez-Garcia,Alain Escassut

Write a review Read reviews Take a Quiz Solve Book Puzzle

Ultrametric Functional Analysis

Seventh International Conference on P-Adic Functional Analysis, June 17-21, 2002, University of Nijmegen, the Netherlands

By: Wilhelmus Hendricus Schikhof,C. Perez-Garcia,Alain Escassut

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

434

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821833200

ISBN 13

9780821833209

Advances in Non-Archimedean Analysis

11th International Conference on P-Adic Functional Analysis, July 5-9 2010, Université Blaise Pascal, Clermont-Ferrand, France

By: Jesus Araujo-Gomez,Bertin Diarra,Alain Escassut

Write a review Read reviews Take a Quiz Solve Book Puzzle

Advances in Non-Archimedean Analysis

11th International Conference on P-Adic Functional Analysis, July 5-9 2010, Université Blaise Pascal, Clermont-Ferrand, France

By: Jesus Araujo-Gomez,Bertin Diarra,Alain Escassut

These collected articles 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 functions spaces, and measure and integration.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

294

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821852914

ISBN 13

9780821852910

Book's by Alain Escassut

Value Distribution In P-adic Analysis

Value Distribution In P-adic Analysis

Ultrametric Functional Analysis

Ultrametric Functional Analysis

Banach Algebras Of Ultrametric Functions

Banach Algebras Of Ultrametric Functions

Analytic Elements in P-adic Analysis

Analytic Elements in P-adic Analysis

A Course in p-adic Analysis

A Course in p-adic Analysis

Ultrametric Banach Algebras

Ultrametric Banach Algebras

Banach Algebras Of Ultrametric Functions

Banach Algebras Of Ultrametric Functions

Value Distribution in P-Adic Analysis

Value Distribution in P-Adic Analysis

P-adic Analytic Functions

P-adic Analytic Functions

Analytic Elements in P-adic Analysis

Analytic Elements in P-adic Analysis

Ultrametric Functional Analysis

Ultrametric Functional Analysis

Advances in Non-Archimedean Analysis

Advances in Non-Archimedean Analysis

Username

Password

Username

Password

Password again

Birthday

Email