Spectral properties of the canonical solution operator to dbar
Complex Variables
2007-05-23 v1 Functional Analysis
Abstract
We study boundedness, compactness, and Schatten-class membership of the canonical solution operator to dbar, 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.
Keywords
Cite
@article{arxiv.math/0612352,
title = {Spectral properties of the canonical solution operator to dbar},
author = {Friedrich Haslinger and Bernhard Lamel},
journal= {arXiv preprint arXiv:math/0612352},
year = {2007}
}