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A representation for the reproducing kernel of a weighted Bergman space

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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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References

  1. Duren, P., Schuster, A.: Bergman Spaces, Mathematical Surveys and Monographs 100. American Mathematical Society, Providence, Rhode Island (2004)

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  1. Department of Mathematics, The University of Mississippi, Hume Hall 305, P.O. Box 1848, University, MS, 38677-1848, USA

    Erwin Miña-Díaz

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  1. Erwin Miña-Díaz
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Correspondence to Erwin Miña-Díaz.

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Miña-Díaz, E. A representation for the reproducing kernel of a weighted Bergman space. Anal.Math.Phys. 13, 58 (2023). https://doi.org/10.1007/s13324-023-00817-7

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  • DOI: https://doi.org/10.1007/s13324-023-00817-7

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