Derivation and integration

書誌事項

Derivation and integration

Washek F. Pfeffer

(Cambridge tracts in mathematics, 140)

Cambridge University Press, 2001

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注記

Includes bibliographical references and index

内容説明・目次

内容説明

This 2001 book is devoted to an invariant multidimensional process of recovering a function from its derivative. It considers additive functions defined on the family of all bounded BV sets that are continuous with respect to a suitable topology. A typical example is the flux of a continuous vector field. A very general Gauss-Green theorem follows from the sufficient conditions for the derivability of the flux. Since the setting is invariant with respect to local lipeomorphisms, a standard argument extends the Gauss-Green theorem to the Stokes theorem on Lipschitz manifolds. In addition, the author proves the Stokes theorem for a class of top-dimensional normal currents - a first step towards solving a difficult open problem of derivation and integration in middle dimensions. The book contains complete and detailed proofs and will provide valuable information to research mathematicians and advanced graduate students interested in geometric integration and related areas.

目次

  • Preface
  • Acknowledgments
  • 1. Preliminaries
  • 2. Charges
  • 3. Variations of charges
  • 4. Charges and BV functions
  • 5. Integration
  • 6. Extending the integral
  • Bibliography
  • List of symbols
  • Index.

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詳細情報

  • NII書誌ID(NCID)
    BA51748804
  • ISBN
    • 0521792681
  • 出版国コード
    uk
  • タイトル言語コード
    eng
  • 本文言語コード
    eng
  • 出版地
    Cambridge
  • ページ数/冊数
    xvi, 266 p.
  • 大きさ
    24 cm
  • 件名
  • 親書誌ID
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