Blaschke product generated covering surfaces

Ilie Barza; Dorin Ghisa

Mathematica Bohemica (2009)

  • Volume: 134, Issue: 2, page 173-182
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Barza, Ilie, and Ghisa, Dorin. "Blaschke product generated covering surfaces." Mathematica Bohemica 134.2 (2009): 173-182. <http://eudml.org/doc/38084>.

@article{Barza2009,
abstract = {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.},
author = {Barza, Ilie, Ghisa, Dorin},
journal = {Mathematica Bohemica},
keywords = {Blaschke product; covering surface; covering transformation; fundamental domain; Cantor set; covering transformation; fundamental domain; Cantor set},
language = {eng},
number = {2},
pages = {173-182},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Blaschke product generated covering surfaces},
url = {http://eudml.org/doc/38084},
volume = {134},
year = {2009},
}

TY - JOUR
AU - Barza, Ilie
AU - Ghisa, Dorin
TI - Blaschke product generated covering surfaces
JO - Mathematica Bohemica
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 134
IS - 2
SP - 173
EP - 182
AB - 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.
LA - eng
KW - Blaschke product; covering surface; covering transformation; fundamental domain; Cantor set; covering transformation; fundamental domain; Cantor set
UR - http://eudml.org/doc/38084
ER -

References

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  1. Ahlfors, L. V., Complex Analysis, International Series in Pure and Applied Mathematics, Mc Graw-Hill Company, Düsseldorf (1979). (1979) Zbl0395.30001MR0510197
  2. Ahlfors, L. V., Sario, L., Riemann Surfaces, Princeton University Press, Princeton N.J. (1960). (1960) Zbl0196.33801MR0114911
  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). (2008) MR2581622
  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). (2007) MR2641555
  5. Cassier, G., Chalendar, I., 10.1080/17476930008815283, Complex Variables, Theory Appl. 42 193-206 (2000). (2000) MR1788126DOI10.1080/17476930008815283
  6. Cao-Huu, T., Ghisa, D., Invariants of infinite Blaschke products, Matematica 45 1-8 (2007). (2007) Zbl1164.30024MR2431141
  7. Constantinescu, C., et al., Integration Theory, Vol. 1, John Wiley & Sons, New York (1985). (1985) 
  8. Garnett, J. B., Bounded Analytic Functions, Academic Press, New York (1981). (1981) Zbl0469.30024MR0628971

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