The canonical solution operator to ?¯ restricted to bergman spaces
- Author(s)
- Friedrich Haslinger
- Abstract
We first show that the canonical solution operator to ?¯ 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 ?¯ restricted to (0, 1)-forms with holomorphic coefficients is a Hubert-Schmidt operator. In the sequel we give a direct proof of the last statement using orthonormal bases and show that in the case of the polydisc and the unit ball in Cn, n > 1, the corresponding operator fails to be a Hubert-Schmidt operator. We also indicate a connection with the theory of Hankel operators. Œ 2001 American Mathematical Society.
- Organisation(s)
- Department of Mathematics
- Journal
- Proceedings of the American Mathematical Society
- Volume
- 129
- Pages
- 3321-3329
- No. of pages
- 9
- ISSN
- 0002-9939
- Publication date
- 2001
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 1010 Mathematics
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/148c3202-bdd6-43f8-9d88-8aeabdc4abad