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Analysis in Positive Characteristic: 178 (Cambridge Tracts in Mathematics, Series Number 178)

Analysis in Positive Characteristic: 178 (Cambridge Tracts in Mathematics, Series Number 178)

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Anatoly N. Kochubei
Cambridge University Press, 3/5/2009
EAN 9780521509770, ISBN10: 0521509777

Hardcover, 220 pages, 23.6 x 16 x 1.5 cm
Language: English

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.

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