Extensions of the Cauchy-Goursat Integral Theorem |
| |
Authors: | Jørgen E Harmse |
| |
Institution: | Sensor Systems, BAE Systems, Building 27-16, 6500 Tracor Lane, Austin, TX 78725, USA |
| |
Abstract: | It is natural to conjecture that if a function f is continuous on the closed region determined by a rectifiable 1-cycle Γ and complex-differentiable on the open region then Γ∫f=0. The main result is an extension of the classical Cauchy-Goursat Theorem: the equality conjectured holds (with no boundary condition on f′) under the additional hypothesis that the winding numbers of Γ define an Lp function and f satisfies a matching Hölder continuity condition near the image of Γ. (In particular, continuity suffices if p=∞.) The proof uses approximations of a rectifiable path by piecewise linear paths. |
| |
Keywords: | Cauchy-Goursat Integral Theorem Approximations of curves |
本文献已被 ScienceDirect 等数据库收录! |
|