Riemann boundary value problem on periodic non-rectifiable curve

Abstract

© 2016 Informa UK Limited, trading as Taylor & Francis Group.We solve the Riemann boundary value problem for holomorphic functions on a periodic non-rectifiable curve. Probably, this is the first study of the Riemann problem on infinite curve, which is not rectifiable. The solution is obtained in terms of generalized integrals over non-rectifiable path.