Journal of Mathematics and Applications
11/42, DOI: 10.7862/rf.2019.11
Finite Blaschke Products and Decomposition
Sümeyra Uçar, Nihal Yılmaz Özgür
DOI: 10.7862/rf.2019.11
Abstract
Let B(z) be a finite Blaschke product of degree n. We consider the problem when a finite Blaschke product can be written as a composition of two nontrivial Blaschke products of lower degree related to the condition B ○ M = B where M is a Möbius transformation from the unit disk onto itself.
References
- R.L. Craighead, F.W. Carroll, A decomposition of finite Blaschke products, Complex Variables Theory Appl. 26 (4) (1995) 333-341.
- U. Daepp, P. Gorkin, R. Mortini, Ellipses and finite Blaschke products, Amer. Math. Monthly 109 (9) (2002) 785-795.
- U. Daepp, P. Gorkin, A. Shaffer, B. Sokolowsky, K. Voss, Decomposing finite Blaschke products, J. Math. Anal. Appl. 426 (2) (2015) 1201-1216.
- U. Daepp, P. Gorkin, K. Voss, Poncelet's theorem, Sendov's conjecture and Blaschke products, J. Math. Anal. Appl. 365 (1) (2010) 93-102.
- L.R. Ford, Automorphic Functions, Second edition, Chelsea Publishing Co., New York, 1951.
- M. Fujimura, Inscribed Ellipses and Blaschke Products, Comput. Methods Funct. Theory 13 (4) (2013) 557-573.
- S.R. Garcia, J. Mashreghi, W.T. Ross, Finite Blaschke products and group theory, in: Finite Blaschke Products and Their Connections, Springer, Cham, 2018, 181-207.
- G. Gassier, I. Chalendar, The group of the invariants of a finite Blaschke products, Complex Variables Theory Appl. 42 (3) (2000) 193-206.
- H.W. Gau, P.Y. Wu, Numerical range and Poncelet property, Taiwanese J. Math. 7 (2) (2003) 173-193.
- A.L. Horwitz, L.A. Rubel, A Uniqueness theorem for monic Blaschke products, Proc. Amer. Math. Soc. 96 (1) (1986) 180-182.
- N. Yılmaz Özgür, Finite Blaschke products and circles that pass through the origin, Bull. Math. Anal. Appl. 3 (3) (2011) 64-72.
- N. Yılmaz Özgür, Some geometric properties of finite Blaschke products, Riemannian Geometry and Applications { Proceedings RIGA 2011, Ed. Univ. Bucureşti, Bucharest, 2011, 239-246.
- N. Yılmaz Özgür, S. Uçar, On some geometric properties of finite Blaschke products, Int. Electron. J. Geom. 8 (2) (2015) 97-105.
About this Article
TITLE:
Finite Blaschke Products and Decomposition
AUTHORS:
Sümeyra Uçar (1)
Nihal Yılmaz Özgür (2)
AUTHORS AFFILIATIONS:
(1) Balıkesir University, TURKEY
(2) Balıkesir University, TURKEY
JOURNAL:
Journal of Mathematics and Applications
11/42
KEY WORDS AND PHRASES:
Finite Blaschke products; Composition of Blaschke products.
FULL TEXT:
http://doi.prz.edu.pl/pl/pdf/jma/88
DOI:
10.7862/rf.2019.11
URL:
http://dx.doi.org/10.7862/rf.2019.11
RECEIVED:
2019-01-24
ACCEPTED:
2019-05-23
COPYRIGHT:
Oficyna Wydawnicza Politechniki Rzeszowskiej, al. Powstańców Warszawy 12, 35-959 Rzeszów