Abstract
Blaschke factorization allows us to write any holomorphic function F as a formal series
where \(a_i \in \mathbb {C}\) and \(B_i\) is a Blaschke product. We introduce a more general variation of the canonical Blaschke product and study the resulting formal series. We prove that the series converges exponentially in the Dirichlet space given a suitable choice of parameters if F is a polynomial and we provide explicit conditions under which this convergence can occur. Finally, we derive analogous properties of Blaschke factorization using our new variable framework.
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Acknowledgements
The authors were supported by the 2018 Summer Math Research at Yale (SUMRY) program. The authors would like to thank Stefan Steinerberger and Hau-Tieng Wu for their endless mentorship and Lihui Tan for helpful feedback on a preliminary draft of this paper.
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Communicated by Daniel Aron Alpay.
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Lukianchikov, M., Nazarchuk, V. & Xue, C. Iterative Variable-Blaschke Factorization. Complex Anal. Oper. Theory 13, 3795–3824 (2019). https://doi.org/10.1007/s11785-019-00931-0
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DOI: https://doi.org/10.1007/s11785-019-00931-0