A finite Blaschke product is a product of finitely many automorphisms of the unit disk. This brief survey covers some of the main topics in the area, including characterizations of Blaschke products, approximation theorems, derivatives and residues of Blaschke products, geometric localization of zeros, and selected other topics.
Copyright © 2018 American Mathematical Society. This conference proceeding first appeared in Harmonic Analysis, Function Theory, Operator Theory, and Their Applications: Conference Proceedings, Bordeaux, June 1-4, 2015, Philippe Jaming, Andreas Hartmann, Karim Kellay, Stanislas Kupin, 133-158, American Mathematical Society, 2018.
The definitive version is available at: American Mathematical Society.
Garcia, Stephan Ramon, Javad Mashreghi, and William T. Ross. "Finite Blaschke Products: A Survey." In Harmonic Analysis, Function Theory, Operator Theory, and Their Applications: Conference Proceedings, Bordeaux, June 1-4, 2015, 133-58. Vol. 22. American Mathematical Society, 2018.
Garcia, Stephan Ramon; Mashreghi, Javad; and Ross, William T., "Finite Blaschke products: a survey" (2018). Math and Computer Science Faculty Publications. 181.