Integration over non-rectifiable curves and Riemann boundary value problems
Integration over non-rectifiable curves and Riemann boundary value problems
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DOI：
10.1016/j.jmaa.2011.02.068
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发表时间：
2011-08
影响因子：
1.3
通讯作者：
R. Abreu‐Blaya;J. Bory‐Reyes;B. Kats
中科院分区：
文献类型：
--
作者：
R. Abreu‐Blaya;J. Bory‐Reyes;B. Kats
在本文中，我们介绍了另一种方法来定义曲线柯西积分的情况下，一个复变函数的不可求长曲线。特别考虑了边界上的跳跃行为。作为应用，在很弱的边界条件下，导出了Riemann边值问题的可解性条件。除了复值函数的情形外，还可以推广到道格拉斯代数值函数的理论。
In this paper we introduce an alternative way of defining the curvilinear Cauchy integral over non-rectifiable curves in the case of complex functions of one complex variable. Especially the jump behavior on the boundary is considered. As an application, solvability conditions of the Riemann boundary value problem are derived on very weak conditions to the boundary. Besides the complex case the consideration can be extended to the theory of Douglis algebra valued functions.