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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