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  1. Home
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  3. Analysis in Positive Characteristic
  • Cited by 7
Publisher:
Cambridge University Press
Online publication date:
October 2009
Print publication year:
2009
Online ISBN:
9780511575624
DOI:
https://doi.org/10.1017/CBO9780511575624
Subjects:
Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Abstract Analysis
Series:
Cambridge Tracts in Mathematics (178)
Information

Book description

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.

Reviews

'… 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.'

Source: Zentralblatt MATH

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