Riemann boundary value problems on the Archimedean spiral

Abstract

This paper studies the Riemann boundary value problems on the Archimedean spiral. We characterize the functions which are integrable on the Archimedean spiral. We also study the asymptotic behaviors of Cauchy-type integral and Cauchy principal value integral on Archimedean spiral at the origin and infinity. At the end, we discuss the Riemann boundary value problems for sectionally holomorphic functions with the Archimedean spiral as their jump curve and obtain the singular integral representations of the solutions if solvable.