| Description |
1 online resource (ix, 210 pages) |
| Series |
Cambridge tracts in mathematics ; 178 |
|
Cambridge tracts in mathematics ; 178.
|
| Contents |
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 |
| Summary |
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, exponential and logarithm, and the orthonormal system of Carlitz polynomials - the author develops a kind of differential and integral calculi. He also expands on the basics of an analytic theory of (Carlitz's) differential equations, providing a useful foundation for the study of various special functions. The differential calculus is extended to a type of Rota's umbral calculus, and an investigation is made of the corresponding rings of differential operators. A theory of quasi-holonomic modules over these rings, having some common features with holonomic modules in the sense of Bernstein, is also connected to some special functions in the spirit of Zeilberger's theory |
| Bibliography |
Includes bibliographical references (pages 203-208) and index |
| Notes |
Print version record |
| Subject |
Mathematical analysis.
|
|
MATHEMATICS -- Calculus.
|
|
MATHEMATICS -- Mathematical Analysis.
|
|
Mathematical analysis
|
| Form |
Electronic book
|
| ISBN |
9780511517778 |
|
0511517777 |
|
9780511515187 |
|
0511515189 |
|
9780511575624 |
|
0511575629 |
|
