论文标题
$ 2^n $的分解blaschke产品
Decomposable Blaschke products of degree $2^n$
论文作者
论文摘要
我们研究了有限的blaschke产品$ b $ 2^n $ $ 2^n $的可分解性 - $ n $ 2 $ 2 $ blaschke产品，检查了Blaschke产品之间的连接，椭圆范围定理，Poncelet定理和Monodromome Group。我们表明，如果换档运算符的压缩的数值范围，$ W（s_b）$，$ b $ a Blaschke able $ n $的产品是椭圆形的，则可以将$ b $写为较低度的Blaschke产品的组成，与Integer $ n $的分解相对应。我们还表明，blaschke的产品$ 2^n $带有椭圆形的blaschke曲线最多具有$ n $不同的临界值，我们用它来检查与正规化的blaschke产品$ b $相关的单片组。我们证明，如果可以将$ b $分解为$ n $ n $ -2 $ blaschke产品，那么与$ b $相关的单片组是$ n $ $ n $ cyclict of $ 2 $的花圈产品。最后，我们研究了Blaschke产品的不变式$ B $ $ 2^n $时，当$ b $是$ n $ blaschke产品$ 2 $的组成。
We study the decomposability of a finite Blaschke product $B$ of degree $2^n$ into $n$ degree-$2$ Blaschke products, examining the connections between Blaschke products, the elliptical range theorem, Poncelet theorem, and the monodromy group. We show that if the numerical range of the compression of the shift operator, $W(S_B)$, with $B$ a Blaschke product of degree $n$, is an ellipse then $B$ can be written as a composition of lower-degree Blaschke products that correspond to a factorization of the integer $n$. We also show that a Blaschke product of degree $2^n$ with an elliptical Blaschke curve has at most $n$ distinct critical values, and we use this to examine the monodromy group associated with a regularized Blaschke product $B$. We prove that if $B$ can be decomposed into $n$ degree-$2$ Blaschke products, then the monodromy group associated with $B$ is the wreath product of $n$ cyclic groups of order $2$. Lastly, we study the group of invariants of a Blaschke product $B$ of order $2^n$ when $B$ is a composition of $n$ Blaschke products of order $2$.
