TY - JOUR
T1 - Integration over non-rectifiable curves and Riemann boundary value problems
AU - Abreu-Blaya, Ricardo
AU - Bory-Reyes, Juan
AU - Kats, Boris A.
N1 - Funding Information:
E-mail addresses: rabreu@facinf.uho.edu.cu (R. Abreu-Blaya), jbory@rect.uo.edu.cu (J. Bory-Reyes), katsboris877@gmail.ru (B.A. Kats). 1 The author is partially supported by Russian Foundation for Basic Researches, grant 11-01-00159-a.
PY - 2011/8/1
Y1 - 2011/8/1
N2 - 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.
AB - 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.
KW - Cauchy integral
KW - Douglis algebra
KW - Fractional dimension
KW - Non-rectifiable curve
KW - Riemann boundary value problem
UR - http://www.scopus.com/inward/record.url?scp=79953693862&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2011.02.068
DO - 10.1016/j.jmaa.2011.02.068
M3 - Artículo
SN - 0022-247X
VL - 380
SP - 177
EP - 187
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -