Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Sub-Bergman spaces in the unit ball of $ \mathbb{C}^n$


Author: Frédéric Symesak
Journal: Proc. Amer. Math. Soc. 138 (2010), 4405-4411
MSC (2010): Primary 32A36; Secondary 46E22
Published electronically: June 10, 2010
MathSciNet review: 2680064
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \Phi(z)=( \varphi_1(z),\cdots,\varphi_l(z))$ be holomorphic from the unit ball of $ \mathbb{C}^n$ into the unit ball of $ \mathbb{C}^l$. We denote by $ B_{\alpha}(z,w)$ the weighted Bergman kernel. We give a condition for the kernel $ (1-\Phi(z){\overline{\Phi(w)}} )B_{\alpha}(z,w)$ to be a reproducing kernel and we study the related Hilbert space.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 32A36, 46E22

Retrieve articles in all journals with MSC (2010): 32A36, 46E22


Additional Information

Frédéric Symesak
Affiliation: Laboratoire de Mathématiques et Application, Université de Poitiers, UMR 6086 CNRS, Téléport 2, Boulevard Pierre et Marie Curie, BP30179, 86962 Futuroscope, France
Email: frederic.symesak@univ-poitiers.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10437-9
PII: S 0002-9939(2010)10437-9
Keywords: Bergman spaces, sub-Hilbert spaces, reproducing kernel
Received by editor(s): November 3, 2009
Received by editor(s) in revised form: February 10, 2010
Published electronically: June 10, 2010
Communicated by: Franc Forstneric
Article copyright: © Copyright 2010 American Mathematical Society