On a boundary property of principal functions
Mineko Watanabe · Pacific Journal of Mathematics · 1969
A behavior of (PjLi-principal functions on some compactifications of a Riemann surface is studied.The main result in this paper is that a (P)Li-principal function is extended almost everywhere continuously to some compactifications and the extention is almost everywhere constant on each part of P. If the genus of the surface is finite and P is the canonical P, (P)Li-principal function can be extended continuously to the Kerekjartό-Stoilow compactification.