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Finite Blaschke Products and Group Theory

In: Finite Blaschke Products and Their Connections

Author

Listed:
  • Stephan Ramon Garcia

    (Pomona College, Department of Mathematics)

  • Javad Mashreghi

    (Laval University, Department of Mathematics and Statistics)

  • William T. Ross

    (University of Richmond, Department of Mathematics and Computer Science)

Abstract

In this chapter we explore two connections between finite Blaschke products and finite group theory. For each finite Blaschke product B, we discuss the group of continuous maps u : 𝕋 → 𝕋 $$u:\mathbb {T}\to \mathbb {T}$$ for which B ∘ u = B on 𝕋 $$\mathbb {T}$$ . We also investigate conditions under which a finite Blaschke product B can be written as the composition of two non-automorphic finite Blaschke products. This is related to the monodromy group associated with B.

Suggested Citation

  • Stephan Ramon Garcia & Javad Mashreghi & William T. Ross, 2018. "Finite Blaschke Products and Group Theory," Springer Books, in: Finite Blaschke Products and Their Connections, chapter 0, pages 181-207, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-78247-8_9
    DOI: 10.1007/978-3-319-78247-8_9
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