This article derives the relation between universal interpolating sequences and some spectral properties of the multiplication operator by the independent variable z in case the underlying space is a Hilbert space of ...This article derives the relation between universal interpolating sequences and some spectral properties of the multiplication operator by the independent variable z in case the underlying space is a Hilbert space of functions analytic on the open unit disk.展开更多
In this paper,{z_(n)}_(n=1)^(∞)acts as an interpolating sequence for Q_(p)∩H^(∞).An analytic function f is constructed,and f(z_(n))=∑_(j)λ_(j)f_(z_(j))(z_(n))=λ_(n),n=1,2,…for any{λ_(n)}∈l~∞,wheref and{λn}...In this paper,{z_(n)}_(n=1)^(∞)acts as an interpolating sequence for Q_(p)∩H^(∞).An analytic function f is constructed,and f(z_(n))=∑_(j)λ_(j)f_(z_(j))(z_(n))=λ_(n),n=1,2,…for any{λ_(n)}∈l~∞,wheref and{λn}∈l^(∞),where f and f_(zj)belong to Q_(p)∩H^(∞).As a result,the study achieves a comparable outcome for F(p,p-2,s)∩H^(∞).展开更多
Let D={z∈: |z|【1} and φ be a normal function on [0, 1). For p∈(0, 1) such a function φ is used to define a Bergman space A^p(φ) on D with weight φ~p(|·|)/(1-|·|~2). In this paper, the dual space of A...Let D={z∈: |z|【1} and φ be a normal function on [0, 1). For p∈(0, 1) such a function φ is used to define a Bergman space A^p(φ) on D with weight φ~p(|·|)/(1-|·|~2). In this paper, the dual space of A^p(φ) is given, four characteristics of Carleson measure on A^p(φ) are obtained. Moreover, as an application, three sequence interpolation theorems in A^p(φ) are derived.展开更多
文摘This article derives the relation between universal interpolating sequences and some spectral properties of the multiplication operator by the independent variable z in case the underlying space is a Hilbert space of functions analytic on the open unit disk.
基金Supported by the National Natural Science Foundation of China(11801347)。
文摘In this paper,{z_(n)}_(n=1)^(∞)acts as an interpolating sequence for Q_(p)∩H^(∞).An analytic function f is constructed,and f(z_(n))=∑_(j)λ_(j)f_(z_(j))(z_(n))=λ_(n),n=1,2,…for any{λ_(n)}∈l~∞,wheref and{λn}∈l^(∞),where f and f_(zj)belong to Q_(p)∩H^(∞).As a result,the study achieves a comparable outcome for F(p,p-2,s)∩H^(∞).
基金Supported by the Doctoral Program Foundation of Institute of Higher Education, P.R. China.
文摘Let D={z∈: |z|【1} and φ be a normal function on [0, 1). For p∈(0, 1) such a function φ is used to define a Bergman space A^p(φ) on D with weight φ~p(|·|)/(1-|·|~2). In this paper, the dual space of A^p(φ) is given, four characteristics of Carleson measure on A^p(φ) are obtained. Moreover, as an application, three sequence interpolation theorems in A^p(φ) are derived.
