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Analysis in Positive Characteristic

£51.00

Part of Cambridge Tracts in Mathematics

  • Date Published: March 2009
  • availability: In stock
  • format: Hardback
  • isbn: 9780521509770

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  • 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.

    • The first treatment of positive characteristic phenomena from the analytic viewpoint
    • Provides a foundation for the study of various special functions
    • For researchers and graduate students in mathematical analysis and number theory
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    Reviews & endorsements

    '… 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

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    Product details

    • Date Published: March 2009
    • format: Hardback
    • isbn: 9780521509770
    • length: 220 pages
    • dimensions: 235 x 160 x 16 mm
    • weight: 0.47kg
    • availability: In stock
  • Table of Contents

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

  • Author

    Anatoly N. Kochubei, National Academy of Sciences of Ukraine
    Anatoly N. Kochubei is head of the department of nonlinear analysis at the Institute of Mathematics, National Academy of Sciences of Ukraine.

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