Geodesic
Factorization of single-valued analytic functions of compact bordered Riemann surfaces
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 17, Tome 170 (1989), pp. 285-313

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This paper conserus a factorization theory of single-valued analytic functions on a compact bordered Riemann surface. The basic ingradient of the theory is a new method to remove the periods of certain functions (natural analogs of Schwartz integrals and Blaschke products) along the boundary curves and crosscuts of the bundles. 
@article{ZNSL_1989_170_a15,
     author = {S. Ya. Khavinson},
     title = {Factorization of single-valued analytic functions of compact bordered {Riemann} surfaces},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {285--313},
     publisher = {mathdoc},
     volume = {170},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1989_170_a15/}
}
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S. Ya. Khavinson. Factorization of single-valued analytic functions of compact bordered Riemann surfaces. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 17, Tome 170 (1989), pp. 285-313. http://geodesic.mathdoc.fr/item/ZNSL_1989_170_a15/