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Line antiderivations over local fields and their applications

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  • S. V. Ludkovsky

Abstract

A non-Archimedean antiderivational line analog of the Cauchy-type line integration is defined and investigated over local fields. Classes of non-Archimedean holomorphic functions are defined and studied. Residues of functions are studied; Laurent series representations are described. Moreover, non-Archimedean antiderivational analogs of integral representations of functions and differential forms such as the Cauchy-Green, Martinelli-Bochner, Leray, Koppelman, and Koppelman-Leray formulas are investigated. Applications to manifold and operator theories are studied.

Suggested Citation

  • S. V. Ludkovsky, 2005. "Line antiderivations over local fields and their applications," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-47, January.
    • Handle: RePEc:hin:jijmms:678131
    DOI: 10.1155/IJMMS.2005.263
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