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arXiv · 2212.08118

A representation for the reproducing kernel of a weighted Bergman space

Erwin Miña-Díaz
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Abstract

For a weight function in the unit disk which is the modulus of a finite product of powers of Blaschke factors, we give a canonical representation for the reproducing kernel of the corresponding weighted Bergman space in terms of the values of the kernel and its derivatives at the origin. This yields a formula for the contractive zero divisor of a Bergman space corresponding to a finite zero set.

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Erwin Miña-Díaz. 2022-12-15. A representation for the reproducing kernel of a weighted Bergman space. https://doi.org/10.1007/s13324-023-00817-7

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