English

Differential Calculus and Integration of Generalized Functions over Membranes

Analysis of PDEs 2008-09-25 v1

Abstract

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

Keywords

Cite

@article{arxiv.0809.4039,
  title  = {Differential Calculus and Integration of Generalized Functions over Membranes},
  author = {J. Aragona and R. Fernandez and S. O. Juriaans and M. Oberguggenberger},
  journal= {arXiv preprint arXiv:0809.4039},
  year   = {2008}
}

Comments

12 pages

R2 v1 2026-06-21T11:23:26.415Z