Abstract:

In this paper, solutions of Riemann boundary value problems with nodes
are extended to the case where they may have singularties of high order at the nodes. Moreover, further extension is discussed when the free term of the problem involved also possesses singularities at the nodes. As an application, certain singular integral equation is discussed.

Key words: Riemann boundary value problem, class K_N, index and canonical
function in class K_N, almost bounded, almost of order k, characteristic singular integral equation