Abstract
In this paper, we consider and study the n-dimensional extension of the Bergman–Dirichlet and Bargmann–Dirichlet spaces introduced recently in El Hamyani et al. (Ann Glob Anal Geom 49(1):59–72, 2016). We give a complete description of the considered spaces, including the explicit closed formulas for their reproducing kernel functions. Moreover, we investigate their asymptotic behavior when the curvature goes to 0.
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Acknowledgements
The assistance of the members of the seminars “Partial differential equations and spectral geometry” is gratefully acknowledged. A. El Fardi, A. Ghanmi and A. Intissar are partially supported by the Hassan II Academy of Sciences and Technology. M. Ziyat is partially supported by the CNRST Grant 56UM5R2015, Morocco.
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El Fardi, A., Ghanmi, A., Intissar, A. et al. Weighted Bergman–Dirichlet and Bargmann–Dirichlet Spaces in High Dimension. Mediterr. J. Math. 14, 166 (2017). https://doi.org/10.1007/s00009-017-0963-1
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DOI: https://doi.org/10.1007/s00009-017-0963-1
Keywords
- Weighted Bergman–Dirichlet spaces
- weighted Bargmann–Dirichlet spaces
- reproducing kernel functions
- hypergeometric functions