Some classes of singular integral equations of convolution type in the class of exponentially increasing functions

Journal of inequalities and applications

Pingrun Li¹ 

关键词: singular integral equations;    Riemann boundary value problems;    dual type;    convolution kernel;    the class of exponentially increasing functions;    45E05;    45E10;    30E25;   

DOI  :  10.1186/s13660-017-1580-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this article, we study some classes of singular integral equations of convolution type with Cauchy kernels in the class of exponentially increasing functions. Such equations are transformed into Riemann boundary value problems on either a straight line or two parallel straight lines by Fourier transformation. We propose one method different from the classical one for the study of such problems and obtain the general solutions and the conditions of solvability. Thus, the result in this paper improves the theory of integral equations and the classical boundary value problems for analytic functions.

【 授权许可】

CC BY