On some spectral properties of the weighted ∂¯-Neumann problem
- Author(s)
- Friedrich Haslinger, Franz Berger
- Abstract
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 Δφj defines a nontrivial doubling measure.
- Organisation(s)
- Department of Mathematics
- Journal
- Kyoto University. Journal of Mathematics
- Volume
- 59
- Pages
- 441-453
- No. of pages
- 13
- ISSN
- 0023-608X
- DOI
- https://doi.org/10.1215/21562261-2019-0013
- Publication date
- 2017
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101002 Analysis, 101008 Complex analysis
- Keywords
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/36b66f76-2dde-4448-9886-4069dbea29a2