Integration over non-rectifiable curves and Riemann boundary value problems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:380

Article

Abreu-Blaya, Ricardo³  Bory-Reyes, Juan²  Kats, Boris A.¹ 

[1] Kazan State Univ Architecture & Civil Engn, Chair Math, Kazan 420043, Russia

[2] Univ Oriente, Dept Matemat, Santiago De Cuba 90500, Cuba

[3] Univ Holguin, Fac Informat & Matemat, Holguin 80100, Cuba

关键词: Non-rectifiable curve;    Fractional dimension;    Cauchy integral;    Douglis algebra;    Riemann boundary value problem;   

DOI  :  10.1016/j.jmaa.2011.02.068

来源: Elsevier

【 摘 要 】

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. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

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