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Onto interpolation for the Dirichlet space and for H1(D)
Advances in Mathematics ( IF 1.5 ) Pub Date : 2021-02-12 , DOI: 10.1016/j.aim.2021.107634 Nikolaos Chalmoukis
中文翻译:
Dirichlet空间和
更新日期:2021-02-12
Advances in Mathematics ( IF 1.5 ) Pub Date : 2021-02-12 , DOI: 10.1016/j.aim.2021.107634 Nikolaos Chalmoukis
We give a characterization of onto interpolating sequences with finite associated measure for the Dirichlet space in terms of condenser capacity. In the Sobolev space we define a natural notion of onto interpolation and we prove that the same condenser capacity condition characterizes all onto interpolating sequences. As a result, for sequences with finite associated measure, the problem of interpolation by an analytic function reduces to a problem of interpolation by a function in .
中文翻译:
Dirichlet空间和
我们用电容器的容量对Dirichlet空间的有限相关度量给出插值序列的刻画。在Sobolev空间我们定义了插值的自然概念,并证明了相同的电容器容量条件可将所有插值序列特征化。结果,对于具有有限关联度量的序列,通过解析函数进行插值的问题减少为通过函数进行插值的问题。。