Spectral properties of the canonical solution operator to d-bar
- Author(s)
- Friedrich Haslinger, Bernhard Lamel
- Abstract
We study boundedness, compactness, and Schatten-class membership of the canonical solution operator to $\bar{\partial}$, restricted to $(0,1)$-forms with holomorphic coefficients, on $L^{2}(d\mu )$ where $\mu $ is a measure with the property that the monomials form an orthogonal family in $L^{2}(d\mu )$. The characterizations are formulated in terms of moment properties of $\mu $. Our results generalize the results of the first author to several variables, contain some known results for several variables, and also cover new ground.
- Organisation(s)
- Department of Mathematics
- Journal
- Journal of Functional Analysis
- Volume
- 255
- Pages
- 13-24
- No. of pages
- 12
- ISSN
- 0022-1236
- Publication date
- 2008
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 1010 Mathematics
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/spectral-properties-of-the-canonical-solution-operator-to-dbar(448b9494-2e60-4311-94bf-27d47bfea18f).html