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| A Characterization of Finite Blaschke Products with Degree n |
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Citation： |
Cailing YAO,Bingzhe HOU,Yang CAO.A Characterization of Finite Blaschke Products with Degree n[J].Chinese Annals of Mathematics B,2025,46(3):407~414 |
| Page view： 110
Net amount： 47 |
Authors： |
Cailing YAO; Bingzhe HOU;Yang CAO |
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| Abstract： |
In this paper, the authors give a characterization of finite Blaschke products
with degree n. The main results are: (1) An n-dimensional complex vector can be the first
n Taylor coefficients of a finite Blaschke product with degree no more than n?1 if and only
if the vector induces a lower triangular Toeplitz matrix with norm 1; (2) an n-dimensional
complex vector can be the first n Taylor coefficients of an inner function if and only if
the vector induces a lower triangular Toeplitz matrix with norm no more than 1. M¨obius
transformations acting on contraction matrices play an important role in the proofs. |
Keywords： |
Finite Blaschke products Toeplitz matrices Contractions Inner functions Taylor coefficients |
Classification： |
30J10, 30J05, 47B35, 47A60, 46E50 |
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