Analytic functionals and the Bergman projection on circular domains

Zorn, Paul

doi:10.1090/S0002-9939-1986-0822427-9

Analytic functionals and the Bergman projection on circular domains
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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.

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