Analysis in Positive Characteristic
Format:Hardback
Publisher:Cambridge University Press
Published:5th Mar '09
Currently unavailable, and unfortunately no date known when it will be back
A treatment of positive characteristic phenomena from an analytic viewpoint.
Devoted to counterparts of classical structures of mathematical analysis in analysis over local fields of positive characteristic, this is one of the first books to treat positive characteristic phenomena from an analytic viewpoint. The author's development of the work begun by Carlitz provides a foundation for studying various special functions.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.
'… 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
ISBN: 9780521509770
Dimensions: 235mm x 160mm x 16mm
Weight: 470g
220 pages