2001/08/06 by Friedrich Haslinger, Haslinger, Friedrich
Mathematics · #32A36 #32W05 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #math.CV #math.FA #msc:32A36 #msc:32W05
paper · pdf · doi:10.48550/arxiv.math/0108035
9 pages
arxiv created 2001/08/06 · arxiv updated 2009/11/30
We first show that the canonical solution operator to d-bar restricted to (0,1)-forms with holomorphic coefficients can be expressed by an integral operator using the Bergman kernel. This result is used to prove that in the case of the unit disc in C the canonical solution operator to d-bar restricted to (0,1)-forms with holomorphic coefficients is a Hilbert-Schmidt operator. In the sequel we give a direct proof of the last statement using orthonormal bases and show that in the case of polydisc and the unit ball in Cn, n>1, the corresponding operator fails to be a Hilbert-Schmidt operator.