关于加权∂¯-Neumann算子的一些谱性质

Pub Date : 2019-01-01 DOI:10.1215/21562261-2019-0013

F. Berger, F. Haslinger

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引用次数: 4

摘要

研究了多元次谐波函数φ在空间L2(Cn, e−φ)上的加权∂-Neumann算子的紧性的必要条件。在假设整个函数对应的加权Bergman空间具有无限维数的情况下，用更简单的方法得到了一个较弱的结果。此外，我们还研究了对于解耦权重的∂- neumann算子的(非)紧性，其形式为φ(z) = φ1(z1) +···+ φn(zn)。如果每一个∆φj定义了一个非平凡的加倍测度，则可以说得更多。

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On some spectral properties of the weighted ∂¯-Neumann operator

We study necessary conditions for compactness of the weighted ∂-Neumann operator on the space L2(Cn, e−φ) for a plurisubharmonic function φ. Under the assumption that the corresponding weighted Bergman space of entire functions has infinite dimension, a weaker result is obtained by simpler methods. Moreover, we investigate (non-) compactness of the ∂-Neumann operator for decoupled weights, which are of the form φ(z) = φ1(z1) + · · ·+ φn(zn). More can be said if every ∆φj defines a nontrivial doubling measure.

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