Reproducing kernel for a class of weighted Bergman spaces on the symmetrized polydisc
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- by Gadadhar Misra, Subrata Shyam Roy and Genkai Zhang PDF
- Proc. Amer. Math. Soc. 141 (2013), 2361-2370 Request permission
Abstract:
A natural class of weighted Bergman spaces on the symmetrized polydisc is isometrically embedded as a subspace in the corresponding weighted Bergman space on the polydisc. We find an orthonormal basis for this subspace. It enables us to compute the kernel function for the weighted Bergman spaces on the symmetrized polydisc using the explicit nature of our embedding. This family of kernel functions includes the Szegö and the Bergman kernel on the symmetrized polydisc.References
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Additional Information
- Gadadhar Misra
- Affiliation: Department of Mathematics, Indian Institute of Science, Bangalore 560 012, India
- Email: gm@math.iisc.ernet.in
- Subrata Shyam Roy
- Affiliation: Indian Institute of Science Education and Research, Kolkata, Mohanpur Campus, Mohanpur (West Bengal) 741 252, India
- Email: ssroy@iiserkol.ac.in
- Genkai Zhang
- Affiliation: Department of Mathematics, Chalmers University of Technology and Gothenburg University, S-412 96 Gothenburg, Sweden
- Email: genkai@chalmers.se
- Received by editor(s): June 20, 2011
- Received by editor(s) in revised form: October 17, 2011
- Published electronically: March 13, 2013
- Additional Notes: Financial support for the work of the first and third authors was provided by the Swedish Research Links programme entitled “Hilbert modules, operator theory and complex analysis”. The research of the first and second authors was funded by grants from DST and UKIERI
- Communicated by: Richard Rochberg
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 2361-2370
- MSC (2010): Primary 30H20, 46E22, 47B32
- DOI: https://doi.org/10.1090/S0002-9939-2013-11514-5
- MathSciNet review: 3043017