THE ESSENTIAL NORMALITY OF Nη-TYPE QUOTIENT MODULE OF HARDY MODULE ON THE POLYDISC
THE ESSENTIAL NORMALITY OF Nη-TYPE QUOTIENT MODULE OF HARDY MODULE ON THE POLYDISC
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发表时间：
2013
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通讯作者：
Penghui Wang
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作者：
Penghui Wang
本文研究了由{ηi（zi）-ηi+1（zi+1）}生成的Nη型商模的本质正规性|i = 1，· · ·，n − 1}，对于内部函数ηi，多圆盘上的哈代模. 1988年，Clark研究了Nη的结构，其中ηi是有限Blaschke积，并由此证明了如果ηi是有限Blaschke积，则Nη是本质正规的。本文证明了要得到Nη的本质正规性，必须满足ηi是有限Blaschke积的条件.
The purpose of this note is to study the essential normality of Nηtype quotient modules, generated by {ηi(zi) − ηi+1(zi+1) | i = 1, · · · , n − 1}, of the Hardy module over the polydisc for inner functions ηi. In 1988, Clark studied the structure of Nη , for which ηi are finite Blaschke products, and as a consequence, Nη is essentially normal if ηi are finite Blaschke products. In this note, we will prove that to obtain the essential normality of Nη , the condition that ηi are finite Blaschke products is necessary.