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 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 , it is also shown that functions which extend holomorphically to a neighborhood of are precisely the Bergman projections of smooth functions whose supports are compact subsets of . 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

Keywords:
Bergman projection,
circular domain,
analytic functional

Article copyright:
© Copyright 1986
American Mathematical Society