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On the classification theory for non-compact Klein surfaces. (English) Zbl 1417.30041

Summary: In this article some classes of Klein surfaces are introduced taking into account the existence of analytic or harmonic functions. For instance, we shall consider the classes \( O_K(HP) \), \( O_K(HB) \) and \( O_K(HD) \) and establish parallel relations among them to the classical case of Riemann surfaces. It is also checked that on Riemann surfaces carrying an antianalytic involution, the theory of principal functions can be developed in a symmetric way so that we can apply these techniques to function theory on Klein surfaces.

MSC:

30F50 Klein surfaces
31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
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References:

[1] Alling, N.; Greenleaf, N., Introduction to the theory of Klein surfaces (1971), Berlin: Springer Verlag, Berlin
[2] Bujalance, E.; Etayo, Jj; Gamboa, Jm; Gromadzki, G., Automorphism groups of compact bordered Klein surfaces (1990), Berlin: Springer Verlag, Berlin · Zbl 0709.14021
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