Line antiderivations over local fields and their applications

2003/12/23 by S. V. Lüdkovsky, S. V. Ludkovsky, Ludkovsky, S. V.
Mathematics · #Advanced Algebra and Geometry #Mathematical Analysis and Transform Methods #advanced mathematical theories #math.CV #msc:46S10

paper · pdf · doi:10.48550/arxiv.math/0312431

53 pages

arxiv created 2003/12/23 · arxiv updated 2009/12/01

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, Lorent 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.

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