International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 2, Pages 263-309

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

Received 23 December 2003

Copyright © 2005 S. V. Ludkovsky. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.