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Author: Alain Escassut
Publisher: World Scientific
ISBN: 9789810222345
Category : Mathematics
Languages : en
Pages : 408
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Book Description
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.
Author: Alain Escassut
Publisher: World Scientific
ISBN: 9789810222345
Category : Mathematics
Languages : en
Pages : 408
Get Book
Book Description
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.
Author: Alain M. Robert
Publisher: Springer Science & Business Media
ISBN: 1475732546
Category : Mathematics
Languages : en
Pages : 451
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Book Description
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: Alain Escassut
Publisher: World Scientific
ISBN: 9811226237
Category : Mathematics
Languages : en
Pages : 349
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Book Description
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.
Author: Alain Escassut
Publisher: World Scientific
ISBN: 9814730114
Category : Mathematics
Languages : en
Pages : 559
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Book Description
"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: Alain Escassut
Publisher: World Scientific
ISBN: 9814730122
Category : Mathematics
Languages : en
Pages : 600
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Book Description
' 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. Contents: Ultrametric FieldsHensel LemmaSpherically Complete ExtensionsAnalytic ElementsPower and Laurent SeriesFactorization of Analytic ElementsDerivative of Analytic ElementsVanishing along a Monotonous FilterMaximum PrincipleQuasi-Invertible Analytic ElementsMeromorphic FunctionsThe Corona Problem on Ab(d(0,1‾))Applications to CurvesGrowth of the Derivative of an Entire FunctionRational Decomposition for Entire Functionsand other papers Readership: Graduate students and researchers interested in p-adic analysis. Keywords:p-Adic;Transcendental Numbers;Meromorphic;Nevalinna Theory'
Author: W.H. Schikhof
Publisher: CRC Press
ISBN: 1000145913
Category : Mathematics
Languages : en
Pages : 419
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Book Description
"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."
Author: N. De Grande-De Kimpe
Publisher: CRC Press
ISBN: 9780824782542
Category : Mathematics
Languages : en
Pages : 350
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Book Description
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.
Author: A.K. Katsaras
Publisher: CRC Press
ISBN: 9780203908143
Category : Mathematics
Languages : en
Pages : 340
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Book Description
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.
Author: Alain Escassut
Publisher: American Mathematical Soc.
ISBN: 1470434911
Category : Functional analysis
Languages : en
Pages : 290
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Book Description
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.
Author: Alain Escassut
Publisher: World Scientific
ISBN: 9812381945
Category : Mathematics
Languages : en
Pages : 291
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Book Description
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.
