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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Analytic functionals and the Bergman projection on circular domains


Author: Paul Zorn
Journal: Proc. Amer. Math. Soc. 96 (1986), 397-401
MSC: Primary 32H10; Secondary 46E20, 46F15
MathSciNet review: 822427
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Abstract: A property of the Bergman projection associated to a bounded circular domain containing the origin in $ {{\mathbf{C}}^N}$ is proved: Functions which extend to be holomorphic in large neighborhoods of the origin are characterized as Bergman projections of smooth functions with small support near the origin. For certain circular domains $ D$, it is also shown that functions which extend holomorphically to a neighborhood of $ \overline D $ are precisely the Bergman projections of smooth functions whose supports are compact subsets of $ D$. Two applications to proper holomorphic mappings are given.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0822427-9
PII: S 0002-9939(1986)0822427-9
Keywords: Bergman projection, circular domain, analytic functional
Article copyright: © Copyright 1986 American Mathematical Society