## Illinois Journal of Mathematics

### Jensen measures and annihilators of holomorphic functions

#### Abstract

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

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

Dates
First available in Project Euclid: 23 February 2010

https://projecteuclid.org/euclid.ijm/1266934798

Digital Object Identifier
doi:10.1215/ijm/1266934798

Mathematical Reviews number (MathSciNet)
MR2594649

Zentralblatt MATH identifier
1188.32004

#### Citation

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. https://projecteuclid.org/euclid.ijm/1266934798

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