Rocky Mountain Journal of Mathematics

Weighted Bergman kernel functions associated to meromorphic functions

Robert Jacobson

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Abstract

We present a technique for computing explicit, concrete formulas for the weighted Bergman kernel on a planar domain with modulus squared weight of a meromorphic function in the case that the meromorphic function has a finite number of zeros on the domain and a concrete formula for the unweighted kernel is known. We apply this theory to the study of the Lu Qi-keng problem.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 1 (2017), 239-257.

Dates
First available in Project Euclid: 3 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1488531898

Digital Object Identifier
doi:10.1216/RMJ-2017-47-1-239

Mathematical Reviews number (MathSciNet)
MR3619762

Zentralblatt MATH identifier
1373.30056

Subjects
Primary: 32A25: Integral representations; canonical kernels (Szego, Bergman, etc.)
Secondary: 32A36: Bergman spaces

Keywords
Bergman kernel function Bergman space

Citation

Jacobson, Robert. Weighted Bergman kernel functions associated to meromorphic functions. Rocky Mountain J. Math. 47 (2017), no. 1, 239--257. doi:10.1216/RMJ-2017-47-1-239. https://projecteuclid.org/euclid.rmjm/1488531898


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