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

• Published in: Journal of inequalities and applications Vol. 2017; no. 1; pp. 1 - 14
• Main Author: Li, Pingrun
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 2017; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Analytic functions; Applications of Mathematics; Boundary value problems; Convolution; convolution kernel; dual type; Fourier transforms; Integral equations; Mathematical analysis; Mathematics; Mathematics and Statistics; Riemann boundary value problems; Singular integral equations; Straight lines; the class of exponentially increasing functions; convolution kernel; singular integral equations; 45E10; dual type; Riemann boundary value problems; the class of exponentially increasing functions; 45E05; 30E25
• ISSN: 1029-242X; 1025-5834; 1029-242X
• DOI: 10.1186/s13660-017-1580-z

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.