Abstract
We introduce new functional spaces generalizing the weighted Bergman and Dirichlet spaces on the complex disk \(\mathbb {D}_R=D(0,R)\) as well as the Bargmann–Fock spaces on the whole complex plane \(\mathbb C\). We give a complete description of the considered spaces. Mainly, we are interested in giving explicit formulas for their reproducing kernel functions and their asymptotic behavior as R goes to infinity.
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Acknowledgments
The authors are thankful to the anonymous referees for their valuable recommendations. The assistance of the members of the seminars “Partial differential equations and spectral geometry” is gratefully acknowledged.
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A. Ghanmi and A. Intissar are partially supported by the Hassan II Academy of Sciences and Technology.
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El Hamyani, A., Ghanmi, A., Intissar, A. et al. Generalized weighted Bergman–Dirichlet and Bargmann–Dirichlet spaces: explicit formulae for reproducing kernels and asymptotics. Ann Glob Anal Geom 49, 59–72 (2016). https://doi.org/10.1007/s10455-015-9480-2
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DOI: https://doi.org/10.1007/s10455-015-9480-2