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Analysis in positive characteristic

Kochubei, Anatoly N.

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Analysis in positive characteristic

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Analysis in positive characteristic/ Anatoly N. Kochubei.
作者:	Kochubei, Anatoly N.
出版者:	Cambridge :Cambridge University Press, : 2009.,
面頁冊數:	ix, 210 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
內容註:	Orthonormal systems and their applications -- Calculus -- Differential equations -- Special functions -- The Carlitz rings.
標題:	Mathematical analysis. -
電子資源:	https://doi.org/10.1017/CBO9780511575624
ISBN:	9780511575624

Analysis in positive characteristic
Kochubei, Anatoly N.

Analysis in positive characteristic[electronic resource] /Anatoly N. Kochubei. - Cambridge :Cambridge University Press,2009. - ix, 210 p. :ill., digital ;24 cm. - Cambridge tracts in mathematics ;178. - Cambridge tracts in mathematics ;178..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Orthonormal systems and their applications -- Calculus -- Differential equations -- Special functions -- The Carlitz rings.

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.

ISBN: 9780511575624Subjects--Topical Terms:

516833
Mathematical analysis.

LC Class. No.: QA300 / .K57 2009

Dewey Class. No.: 515

Analysis in positive characteristic
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505 0 $a Orthonormal systems and their applications -- Calculus -- Differential equations -- Special functions -- The Carlitz rings.
520 $a 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.
650 0 $a Mathematical analysis. $3 516833
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830 0 $a Cambridge tracts in mathematics ; $v 178. $3 3470486
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