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Keywords:
Blaschke product; covering surface; covering transformation; fundamental domain; Cantor set
Blaschke product; covering surface; covering transformation; fundamental domain; Cantor set
Summary:
It is known that, under very general conditions, Blaschke products generate branched covering surfaces of the Riemann sphere. We are presenting here a method of finding fundamental domains of such coverings and we are studying the corresponding groups of covering transformations.
References:
[1] Ahlfors, L. V.: Complex Analysis. International Series in Pure and Applied Mathematics, Mc Graw-Hill Company, Düsseldorf (1979). MR 0510197 | Zbl 0395.30001
[2] Ahlfors, L. V., Sario, L.: Riemann Surfaces. Princeton University Press, Princeton N.J. (1960). MR 0114911 | Zbl 0196.33801
[3] Barza, I., Ghisa, D.: The Geometry of Blaschke Product Mappings. Further Progress in Analysis, World Scientific H. G. W. Begehr, A. O. Celebi, R. P. Gilbert (2008). MR 2581622
[4] Barza, I., Ghisa, D.: Blaschke Self-Mappings of the Real Projective Plane. The Procedings of the 6-th Congress of Romanian Mathematiciens, Bucharest (2007). MR 2641555
[5] Cassier, G., Chalendar, I.: The group of invariants of a finite Blaschke product. Complex Variables, Theory Appl. 42 193-206 (2000). DOI 10.1080/17476930008815283 | MR 1788126
[6] Cao-Huu, T., Ghisa, D.: Invariants of infinite Blaschke products. Matematica 45 1-8 (2007). MR 2431141 | Zbl 1164.30024
[7] Constantinescu, C., et al.: Integration Theory, Vol. 1. John Wiley & Sons, New York (1985).
[8] Garnett, J. B.: Bounded Analytic Functions. Academic Press, New York (1981). MR 0628971 | Zbl 0469.30024
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