Illinois Journal of Mathematics

Jensen measures and annihilators of holomorphic functions

Nihat Gogus and Evgeny A. Poletsky

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For a relatively compact domain $M$ in a complex manifold, we completely characterize in terms of Jensen measures the annihilating measures of the algebra $A(\overline M)$ of holomorphic functions and the space $h(\overline M)$ of pluriharmonic functions continuous on $\overline M$. We also establish the equivalence of Mergelyan type approximation properties of a domain for different function spaces.

Article information

Illinois J. Math., Volume 53, Number 2 (2009), 679-690.

First available in Project Euclid: 23 February 2010

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Zentralblatt MATH identifier

Primary: 32A38: Algebras of holomorphic functions [See also 30H05, 46J10, 46J15] 32U05: Plurisubharmonic functions and generalizations [See also 31C10]


Gogus, Nihat; Poletsky, Evgeny A. Jensen measures and annihilators of holomorphic functions. Illinois J. Math. 53 (2009), no. 2, 679--690. doi:10.1215/ijm/1266934798.

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