International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 2, Pages 263-309
doi:10.1155/IJMMS.2005.263
Line antiderivations over local fields and their applications
S.V. Ludkovsky
Theoretical Department, Institute of General Physics, Russian Academy of Sciences, 38 Vavilov Street, Moscow 119991, GSP-1, Russia
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.