| Title:
|
Blaschke product generated covering surfaces (English) |
| Author:
|
Barza, Ilie |
| Author:
|
Ghisa, Dorin |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
134 |
| Issue:
|
2 |
| Year:
|
2009 |
| Pages:
|
173-182 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Blaschke product |
| Keyword:
|
covering surface |
| Keyword:
|
covering transformation |
| Keyword:
|
fundamental domain |
| Keyword:
|
Cantor set |
| MSC:
|
14H30 |
| MSC:
|
30D50 |
| idZBL:
|
Zbl 1212.30158 |
| idMR:
|
MR2535145 |
| DOI:
|
10.21136/MB.2009.140652 |
| . |
| Date available:
|
2010-07-20T17:56:41Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140652 |
| . |
| Reference:
|
[1] Ahlfors, L. V.: Complex Analysis.International Series in Pure and Applied Mathematics, Mc Graw-Hill Company, Düsseldorf (1979). Zbl 0395.30001, MR 0510197 |
| Reference:
|
[2] Ahlfors, L. V., Sario, L.: Riemann Surfaces.Princeton University Press, Princeton N.J. (1960). Zbl 0196.33801, MR 0114911 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[5] Cassier, G., Chalendar, I.: The group of invariants of a finite Blaschke product.Complex Variables, Theory Appl. 42 193-206 (2000). MR 1788126, 10.1080/17476930008815283 |
| Reference:
|
[6] Cao-Huu, T., Ghisa, D.: Invariants of infinite Blaschke products.Matematica 45 1-8 (2007). Zbl 1164.30024, MR 2431141 |
| Reference:
|
[7] Constantinescu, C., et al.: Integration Theory, Vol. 1.John Wiley & Sons, New York (1985). |
| Reference:
|
[8] Garnett, J. B.: Bounded Analytic Functions.Academic Press, New York (1981). Zbl 0469.30024, MR 0628971 |
| . |
