The canonical solution operator to d-bar restricted to Bergman spaces

Simple item page
dc.creatorHaslinger, Friedrich
dc.date2001-08-06
dc.date.accessioned2026-07-07T04:42:53Z
dc.date.available2026-07-07T04:42:53Z
dc.descriptionWe 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 C^n, n>1, the corresponding operator fails to be a Hilbert-Schmidt operator.
dc.description9 pages
dc.identifierhttps://arxiv.org/abs/math/0108035
dc.identifierhttp://arxiv.org/abs/math/0108035
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61974
dc.subjectComplex Variables
dc.subjectFunctional Analysis
dc.subject32W05; 32A36
dc.titleThe canonical solution operator to d-bar restricted to Bergman spaces
dc.typetext

Files

Collections

arXiv