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Pairs of inner functions on finite Riemann surfaces

Pairs of inner functions on finite Riemann surfaces

I. Introduction.A finite (open) Riemann surface R is a connected open proper subset of some compact Riemann surface X such that the boundary 8R of 7? is also the boundary of its closure R and is the union of finitely many disjoint simple closed analytic curves I\,..., Tk.It is clear …