TY  - GEN
AU  - Kochubei, Anatoly N.
TI  - Analysis in positive characteristic
SN  - 9780521509770
U1  - 515 
PY  - 2009///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Mathematical analysis
KW  - Local fields--Algebra
KW  - Calculus
KW  - Differential Equations
KW  - Carlitz Rings
N1  - Includes references and index
N2  - 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.

https://www.cambridge.org/core/books/analysis-in-positive-characteristic/878A716A22462F0F187AA64710C73072#fndtn-information
ER  -