On the failure of canonical factorization in lAp

被引：3
|
作者：
Cheng, Raymond [1 ]
Dragas, James G. [1 ]
机构：
[1] Old Dominion Univ, Dept Math & Stat, Norfolk, VA 29529 USA
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2019年 / 479卷 / 02期
关键词：
Canonical factorization; Inner function; Zero set; INVARIANT SUBSPACES; INNER FUNCTIONS; PREDICTION; SPACES;
D O I：
10.1016/j.jmaa.2019.07.033
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
It is shown by construction that for some values of p, there exists a polynomial f is an element of l(A)(P) such that f fails to factorize as f = JG, where J is p-inner, and G is analytic and nonvanishing in the open unit disk D. In this situation, any p-inner function J vanishing at the roots of f in D, with multiplicities taken into account, must also vanish at some other point of D. It is shown that any such "extra zeros" of J must lie close to the boundary of the disk. (C) 2019 Elsevier Inc. All rights reserved.
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页码：1939 / 1955
页数：17
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