Factorization of univalent analytic functions on compact Riemann surfaces with boundary

The paper is devoted to the theory of factorization of univalent analytic functions on a compact Riemann surface with boundary. The main component of the theory is a new method for the removal of the periods of certain functions (the natural analogues of the Schwarz integral and Blaschke products) along the boundary curves and bundle sections.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 170, pp. 285–313, 1989.