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Spectral Theory of Magnetic Berezin Transforms on the Complex Projective Space

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Abstract

We define magnetic Berezin transforms on the complex projective space \(P(\mathbb {C}^{n})\) and we give a formula representing these transforms as functions of the Fubini–Study Laplacian. Then, we study their \(L^2\)-spectral theory. As an application, we propose an arithmetic formula for the linearization coefficients of some Jacobi polynomials.

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Acknowledgements

The assistance of the members of the seminars “Partial differential equations and spectral geometry” is gratefully acknowledged, specially Adil Belhaj for his helpful discussion. We also would like to thank the anonymous referee for the helpful remarks and questions related to the content.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences and Technics (M’Ghila), Sultan My Slimane University, Beni Mellal, Morocco

    Nour Eddine Askour

  2. P.D.E. and Spectral Geometry, Laboratory of Analysis and Applications - URAC/03, Department of Mathematics, Faculty of Sciences, Mohammed V University, P.O. Box 1014, Rabat, Morocco

    Ahmed Intissar & Mohammed Ziyat

Authors
  1. Nour Eddine Askour
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  2. Ahmed Intissar
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  3. Mohammed Ziyat
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Corresponding author

Correspondence to Nour Eddine Askour.

Additional information

Communicated by Behrndt, Colombo and Naboko.

In memory of Professeur Ahmed Intissar (1952–2017).

M. Ziyat is partially supported by the CNRST Grant 56UM5R2015, Morocco.

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Askour, N.E., Intissar, A. & Ziyat, M. Spectral Theory of Magnetic Berezin Transforms on the Complex Projective Space. Complex Anal. Oper. Theory 12, 705–727 (2018). https://doi.org/10.1007/s11785-017-0738-5

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  • DOI: https://doi.org/10.1007/s11785-017-0738-5

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