Line antiderivations over local fields and their applications

Details Line antiderivations over local fields and their applications Line antiderivations over local fields and their applications

2003-12-23

arxiv.org/abs/math/0312431v1

Mathematics

Complex Variables

53 pages

Scientific paper

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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