http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
- 中文 을 입력하시려면 zhongwen을 입력하시고 space를누르시면됩니다.
- 北京 을 입력하시려면 beijing을 입력하시고 space를 누르시면 됩니다.
RISS 인기검색어
- 검색키워드
- 저자 : Pavicevic, (검색결과 2 건)
- 무료
- 기관 내 무료
- 유료
-
WEAKLY DENSE IDEALS IN PRIVALOV SPACES OF HOLOMORPHIC FUNCTIONS
Mestrovic, Romeo,Pavicevic, Zarko Korean Mathematical Society 2011 대한수학회지 Vol.48 No.2
In this paper we study the structure of closed weakly dense ideals in Privalov spaces $N^p$ (1 < p < $\infty$) of holomorphic functions on the disk $\mathbb{D}$ : |z| < 1. The space $N^p$ with the topology given by Stoll's metric [21] becomes an F-algebra. N. Mochizuki [16] proved that a closed ideal in $N^p$ is a principal ideal generated by an inner function. Consequently, a closed subspace E of $N^p$ is invariant under multiplication by z if and only if it has the form $IN^p$ for some inner function I. We prove that if $\cal{M}$ is a closed ideal in $N^p$ that is dense in the weak topology of $N^p$, then $\cal{M}$ is generated by a singular inner function. On the other hand, if $S_{\mu}$ is a singular inner function whose associated singular measure $\mu$ has the modulus of continuity $O(t^{(p-1)/p})$, then we prove that the ideal $S_{\mu}N^p$ is weakly dense in $N^p$. Consequently, for such singular inner function $S_{\mu}$, the quotient space $N^p/S_{\mu}N^p$ is an F-space with trivial dual, and hence $N^p$ does not have the separation property.
-
WEAKLY DENSE IDEALS IN PRIVALOV SPACES OF HOLOMORPHIC FUNCTIONS
Romeo Mestrovic,Zarko Pavicevic 대한수학회 2011 대한수학회지 Vol.48 No.2
In this paper we study the structure of closed weakly dense ideals in Privalov spaces N^p (1 < p < ∞) of holomorphic functions on the disk D : <수식>. The space Np with the topology given by Stoll's metric [21] becomes an F-algebra. N. Mochizuki [16] proved that a closed ideal in N^p is a principal ideal generated by an inner function. Consequently,a closed subspace E of N^p is invariant under multiplication by z if and only if it has the form IN^p for some inner function I. We prove that if M is a closed ideal in Np that is dense in the weak topology of N^p, then M is generated by a singular inner function. On the other hand, if Sμis a singular inner function whose associated singular measure μ has the modulus of continuity <수식> then we prove that the ideal SμN^p is weakly dense in N^p. Consequently, for such singular inner function Sμ,the quotient space N^p=SμN^p is an F-space with trivial dual, and hence N^p does not have the separation property.
연관 검색어 추천
이 검색어로 많이 본 자료
활용도 높은 자료
