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Analysis in Positive Characteristic: Cambridge Tracts in Mathematics, cartea 178

Autor Anatoly N. Kochubei
en Limba Engleză Hardback – 5 mar 2009
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.
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Specificații

ISBN-13: 9780521509770
ISBN-10: 0521509777
Pagini: 220
Dimensiuni: 160 x 235 x 16 mm
Greutate: 0.46 kg
Ediția:New.
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Cambridge Tracts in Mathematics

Locul publicării:Cambridge, United Kingdom

Cuprins

Preface; 1. Orthonormal systems and their applications; 2. Calculus; 3. Differential equations; 4. Special functions; 5. The Carlitz rings; Bibliography; Index.

Recenzii

'… beautifully written, discuses some fascinating topics and its is surprisingly easy to read in view of the enormous amount of material presented in less than 200 pages.' Zentralblatt MATH

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Descriere

A treatment of positive characteristic phenomena from an analytic viewpoint.