Analysis in positive characteristic /

Devoted to counterparts of classical structures of mathematical analysis in analysis over local fields of positive characteristic, this book treats positive characteristic phenomena from an analytic viewpoint. Building on the basic objects introduced by L. Carlitz - such as the Carlitz factorials, e...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Kochubei, Anatoly N.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge, UK ; New York : Cambridge Univ. Press, ©2009.
Colección:Cambridge tracts in mathematics ; 178.
Temas:
Mathematical analysis.
Analyse mathématique.
MATHEMATICS > Calculus.
MATHEMATICS > Mathematical Analysis.
Mathematical analysis
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Half-title
  • Title
  • Copyright
  • Contents
  • Preface
  • 1 Orthonormal systems and their applications
  • 1.1 Basic notions
  • 1.2 Additive Carlitz polynomials
  • 1.3 Hyperdifferentiations
  • 1.4 The digit principle
  • 1.5 Finite places of a global function field
  • 1.6 The Carlitz module
  • 1.7 Canonical commutation relations
  • 1.8 Comments
  • 2 Calculus
  • 2.1 Fq-Linear calculus
  • 2.2 Umbral calculus
  • 2.3 Locally analytic functions
  • 2.4 General smooth functions
  • 2.5 Entire functions
  • 2.6 Measures and divided power series
  • 3 Differential equations
  • 3.1 Existence and uniqueness theorems
  • 3.2 Strongly nonlinear equations
  • 3.3 Regular singularity
  • 3.4 Evolution equations
  • 3.5 Comments
  • 4 Special functions
  • 4.1 Hypergeometric functions
  • 4.2 Analogs of the Bessel functions and Jacobi polynomials
  • 4.3 Polylogarithms
  • 4.4 K-binomial coefficients
  • 4.5 Overconvergence properties
  • 4.6 Comments
  • 5 The Carlitz rings
  • 5.1 Algebraic preliminaries
  • 5.2 The Carlitz rings
  • 5.3 The ring A1
  • 5.4 Quasi-holonomic modules
  • 5.5 Comments
  • Bibliography
  • Index.

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