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June 2019 On some spectral properties of the weighted ¯-Neumann operator
Franz Berger, Friedrich Haslinger
Kyoto J. Math. 59(2): 441-453 (June 2019). DOI: 10.1215/21562261-2019-0013

Abstract

We study necessary conditions for compactness of the weighted ¯-Neumann operator on the space L2(Cn,eφ) 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 Δφj defines a nontrivial doubling measure.

Citation

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Franz Berger. Friedrich Haslinger. "On some spectral properties of the weighted ¯-Neumann operator." Kyoto J. Math. 59 (2) 441 - 453, June 2019. https://doi.org/10.1215/21562261-2019-0013

Information

Received: 17 October 2016; Revised: 1 April 2017; Accepted: 3 April 2017; Published: June 2019
First available in Project Euclid: 27 April 2019

zbMATH: 07080112
MathSciNet: MR3960301
Digital Object Identifier: 10.1215/21562261-2019-0013

Subjects:
Primary: 32W05
Secondary: 35N15, 35P05, 47F05

Rights: Copyright © 2019 Kyoto University

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Vol.59 • No. 2 • June 2019
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