Differential Calculus and Integration of Generalized Functions over Membranes
Aragona, J. ; Fernandez, R. ; Juriaans, S. O. ; Oberguggenberger, M.
arXiv, 0809.4039 / Harvested from arXiv
Text on arXiv
In this paper we continue the development of the differential calculus started by Aragona-Ferandez-Juriaans. Guided by the topology introduced recently by those authors we introduce the notion of membranes and extend the definition of integrals given in [2] to integrals defined on membranes. We use this to prove a generalized version of teh Cauchy formula and to obtain the Goursat Theorem for generalized holomorphic functions. We also show that the generalized transport equation can be solved giving an explicit solution
Publié le : 2008-09-23
Classification:  Mathematics - Analysis of PDEs,  46F30,  46T20 
@article{0809.4039,
     author = {Aragona, J. and Fernandez, R. and Juriaans, S. O. and Oberguggenberger, M.},
     title = {Differential Calculus and Integration of Generalized Functions over
  Membranes},
     journal = {arXiv},
     volume = {2008},
     number = {0},
     year = {2008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0809.4039}
}

Aragona, J.; Fernandez, R.; Juriaans, S. O.; Oberguggenberger, M. Differential Calculus and Integration of Generalized Functions over
  Membranes. arXiv, Tome 2008 (2008) no. 0, . http://gdmltest.u-ga.fr/item/0809.4039/