## Analytic functionals and the Bergman projection on circular domains

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- by Paul Zorn PDF
- Proc. Amer. Math. Soc.
**96**(1986), 397-401 Request permission

## 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.## References

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## Additional Information

- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**96**(1986), 397-401 - MSC: Primary 32H10; Secondary 46E20, 46F15
- DOI: https://doi.org/10.1090/S0002-9939-1986-0822427-9
- MathSciNet review: 822427