Asymptotics of reproducing kernels on a plane domain
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- by Miroslav Engliš PDF
- Proc. Amer. Math. Soc. 123 (1995), 3157-3160 Request permission
Abstract:
Let $\Omega$. be a plane domain of hyperbolic type, $|dz|/w(z)$ the Poincaré metric on $\Omega$, and ${K_{\Omega ,q}}(x,\bar y)$ the reproducing kernel for the Hilbert space $\mathcal {A}_q^2(\Omega )$ of all holomorphic functions on $\Omega$ square-integrable with respect to the measure $w{(z)^{2q - 2}}|dz \wedge d\bar z|$. It is proved that \[ \lim \limits _{q \to + \infty } \frac {{{K_{\Omega ,q}}(z,\bar z)w{{(z)}^{2q}}}}{{2q}} = \frac {1}{\pi }.\]References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 3157-3160
- MSC: Primary 30C40; Secondary 30E15, 46E22
- DOI: https://doi.org/10.1090/S0002-9939-1995-1277107-0
- MathSciNet review: 1277107